共查询到20条相似文献,搜索用时 31 毫秒
1.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2011,121(2):171-179
In this paper, we classify real hypersurfaces in the complex projective space
C P\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector
fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field. 相似文献
2.
We study some special almost complex structures on strictly pseudoconvex domains in ℝ2
n
. They appear naturally as limits under a nonisotropic scaling procedure and play a role of model objects in the geometry
of almost complex manifolds with boundary. We determine explicitely some geometric invariants of these model structures and
derive necessary and sufficient conditions for their integrability. As applications we prove a boundary extension and a compactness
principle for some elliptic diffeomorphisms between relatively compact domains. 相似文献
3.
We describe Bott towers as sequences of toric manifolds Mk, and identify the omniorientations which correspond to their original construction as complex varieties. We show that the suspension of Mk is homotopy equivalent to a wedge of Thom complexes, and display its complex K-theory as an algebra over the coefficient ring. We extend the results to KO-theory for several families of examples, and compute the effects of the realification homomorphism; these calculations breathe geometric life into Bahri and Benderskys analysis of the Adams Spectral Sequence [Bahri, A. and Bendersky, M.: The KO-theory of toric manifolds. Trans. Am. Math. Soc. 352 (2000), 1191–1202.] By way of application we consider the enumeration of stably complex structures on Mk, obtaining estimates for those which arise from omniorientations and those which are almost complex. We conclude with observations on the rôle of Bott towers in complex cobordism theory.Mathematics Subject Classification (2000): 55R25, 55R50, 57R77.(Received: August 2004) 相似文献
4.
We consider a generalization of Einstein–Sasaki manifolds, which we characterize in terms both of spinors and differential
forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable
examples in seven dimensions. Then, we consider circle actions that preserve the structure and determine conditions for the
contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact
structure on S
2 × T
3. 相似文献
5.
We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r=2 and r=3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r=2,3 and 4 respectively, several classes of 8-dimensional manifolds (for 5?r?8), families of real, complex and quaternionic Grassmannians (for r=8,6 and 5 respectively), and Rosenfeld?s elliptic projective planes OP2, (C⊗O)P2, (H⊗O)P2 and (O⊗O)P2, which are symmetric spaces associated to the exceptional simple Lie groups F4, E6, E7 and E8 (for r=9,10,12 and 16 respectively). As an application, we classify all Riemannian manifolds whose metric is bundle-like along the curvature constancy distribution, generalizing well-known results in Sasakian and 3-Sasakian geometry. 相似文献
6.
We generalize Bangert’s non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic ℝ2n
to asymptotically standard symplectic manifolds. 相似文献
7.
Telemachos Hatziafratis 《Annali di Matematica Pura ed Applicata》1989,154(1):327-340
Summary An explicit Koppelman-Leray-Norguet type integral formula for differential forms is derived on generalized analytic polyhedra on complex manifolds which arise as analytic subvarieties of domains ofC
n. Using this formula we give an explicit solution operator to the
-equation on strictly pseudoconvex polyhedra in that setting and we prove that this solution operator admits uniform estimates. 相似文献
8.
Renyi Ma 《manuscripta mathematica》1998,95(2):159-168
If (N, ο, J,g) is an almost K?hler manifold and M is a branched minimal immersion which is not a $J$-holomorphic curve, we show that the complex tangents are isolated and
that each has a negative index, which extends the results in the K?hler case by S. S. Chern and J. Wolfson [2] and S. Webster
[7] to almost K?hler manifolds. As an application, we get lower estimates for the genus of embedded minimal surfaces in almost
K?hler manifolds. The proofs of these results are based on the well-known Cartan's moving frame methods as in [2, 7]. In our
case, we must compute the torsion of the almost complex structures and find a useful representation of torsion. Finally, we
prove that the minimal surfaces in complex projective plane with any almost complex structure is a J-holomorphic curve if it is homologous to the complex line.
Received: 10 January 1997 / Revised version: 22 August 1997 相似文献
9.
《复变函数与椭圆型方程》2012,57(10):939-951
Let Ω be a bounded, weakly pseudoconvex domain in C n , n ≤ 2, with real-analytic boundary. A real-analytic submanifold M ? ?Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to (Ω¯). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of ?Ω. 相似文献
10.
Special properties of realizations of supersymmetry on noncompact manifolds are discussed. On the basis of the supersymmetric
scattering theory and the supersymmetric trace formulas, the absolute or relative Euler characteristic of a barrier inR
N can be obtained from the scattering data for the Laplace operator on forms with absolute or relative boundary conditions.
An analog of the Chern-Gauss-Bonnet theorem for noncompact manifolds is also obtained. The map from the stationary curve of
an antiholomorphic involution on a compact Riemann surface to the real circle on the Riemann sphere, generated by a real meromorphic
function is considered. An analytic expression for its topological index is obtained by using supersymmetric quantum mechanics
with meromorphic superpotential on the Klein surface. Bibliography: 27 titles.
Dedicated to L. D. Faddeev on the occasion of his 60th birthday
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 215, 1994, pp. 77–99.
Translated by B. M. Bekker. 相似文献
11.
V. K. Beloshapka V. V. Ezhov G. Schmalz 《Proceedings of the Steklov Institute of Mathematics》2006,253(1):1-7
We study real analytic CR manifolds of CR dimension 1 and codimension 2 in the three-dimensional complex space. We prove that the germ of a holomorphic mapping between “nonspherical” manifolds can be extended along any path (this is an analog of Vitushkin’s germ theorem). For a cubic model surface (“sphere”), we prove an analog of the Poincaré theorem on the mappings of spheres into ?2. We construct an example of a compact “spherical” submanifold in a compact complex 3-space such that the germ of a mapping of the “sphere” into this submanifold cannot be extended to a certain point of the “sphere.” 相似文献
12.
S. V. Ludkovsky 《Journal of Mathematical Sciences》2007,141(3):1331-1384
This paper is devoted to the investigation of semidirect products of loop groups and homeomorphism or diffeomorphism groups
of finite-and infinite-dimensional real, complex, and quaternion manifolds. Necessary statements about quaternion manifolds
with quaternion holomorphic transition mappings between charts of atlases are proved. It is shown that these groups exist
and have the structure of infinite-dimensional Lie groups, i.e., they are continuous or differentiable manifolds and the composition
(f, g) ↦ f
−1
g is continuous or differentiable depending on the smoothness class of groups. Moreover, it is proved that in the cases of
complex and quaternion manifolds, these groups have the structures of complex and quaternion manifolds, respectively. Nevertheless,
it is proved that these groups do not necessarily satisfy the Campbell-Hausdorff formula even locally outside of the exceptional
case of a group of holomorphic diffeomorphisms of a compact complex manifold. Unitary representations of these groups G′, including irreducible ones, are constructed by using quasi-invariant measures on groups G relative to dense subgroups G′. It is proved that this procedure provides a family of cardinality card(ℝ) of pairwise nonequivalent, irreducible, unitary
representations. The differentiabilty of such representations is studied.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 28, Algebra
and Analysis, 2005. 相似文献
13.
We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds (see Theorem 1.1). The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinitesimal pseudometric and on the scaling method in almost complex manifolds.Mathematics Subject Classification (2000): 32H02,53C15 相似文献
14.
M. Verbitsky 《Selecta Mathematica, New Series》1998,4(3):447-490
Let M be a compact complex manifold equipped with a hyperk?hler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i.e., complex analytic with respect to all complex structures induced by the hyperk?hler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trianalytic subvarieties. We prove
that all deformations of X are trianalytic and naturally isomorphic to X as complex analytic varieties. We show that this isomorphism is compatible with the metric induced from M. Also, we prove that the Douady space of complex analytic deformations of X in M is equipped with a natural hyperk?hler structure. 相似文献
15.
Two constructions of contact manifolds are presented: (i) products of S
1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic
circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, we can
show that all closed, oriented 5-manifolds that are Cartesian products of lower-dimensional manifolds carry a contact structure.
For symplectic 4-manifolds we exhibit an alternative construction of such a decomposition; this gives us control over the
homotopy type of the corresponding contact structure. In particular, we prove that
\mathbb CP2×S1{{\mathbb {CP}}^2\times S^1} admits a contact structure in every homotopy class of almost contact structures. The existence of contact structures is also
established for a large class of 5-manifolds with fundamental group
\mathbbZ2{{\mathbb{Z}}_2} . 相似文献
16.
Anand Dessai 《Mathematische Nachrichten》1998,192(1):159-172
In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H1(M;?) = 0 and no 2-torsion in H1(M;?) for i = 2,3. Using the Classification Theorem of Donaldson we give a reformulation of the conditions for a 4-manifold to be almost complex in terms of Betti numbers and the dimension of the ±-eigenspaces of the intersection form. In the second part we give general conditions for an almost complex manifold to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete intersections. 相似文献
17.
Adam Harris 《Journal of Geometric Analysis》1995,5(4):533-550
Let ƒ:M →D ⊑C
n
be a holomorphic family of compact, complex surfaces, which is locally trivial onD∖Z, for an analytic subsetZ. Conditions are found under which ƒ extends trivially toD, if the fibers of ƒ|D∖Z are either Hirzebruch surfaces (projective bundles overP
1), Hopf surfaces (elliptic bundles overP
1), hyperelliptic bundles, or any compact complex surface having one of these as minimal model under blowing-down. The results
of this paper are motivated by the existence of non-Hausdorff moduli spaces in the deformation of complex structure for certain
complex manifolds. 相似文献
18.
We study m-dimensional real submanifolds M with (m − 1)-dimensional maximal holomorphic tangent subspace in complex projective space. On these manifolds there exists an almost
contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX, Y) − h(X, FY) = g(FX, Y)η, η ∈ T
⊥(M), on the almost contact structure F and on the second fundamental form h of these submanifolds and we characterize certain model spaces in complex projective space. 相似文献
19.
Stefano Trapani 《Journal of Geometric Analysis》2000,10(4):739-758
Let S be a generic submanifold of
C
N
of real codimension m. In this paper we continue the study, carried over by various authors, of the set of analytic discs
attached to S. Moreover, we look at the subspaces of
C
N
obtained by evaluating at given points, holomorphic maps which are infinitesimal deformations of analytic discs attached to
S. 相似文献
20.
Goutam Mukherjee 《Proceedings Mathematical Sciences》1995,105(4):381-391
We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS
1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly. 相似文献