共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we give the spherical characterization of a regular curve in 3-dimensional Sasakian space. Furthermore the differential equation which expresses the mentioned characterization is solved. 相似文献
2.
Yueshan XIONG 《Frontiers of Mathematics in China》2015,10(2):395
The homotopy connectedness theorem for invariant immersions in Sasakian manifolds with nonnegative transversal q-bisectional curvature is proved. Some Barth-Lefschetz type theorems for minimal submanifolds and (k, ?)-saddle submanifolds in Sasakian manifolds with positive transversal q-Ricci curvature are proved by using the weak (?-)asymptotic index. As a corollary, the Frankel type theorem is proved. 相似文献
3.
We first generalize the join construction described previously by the first two authors [4] for quasi-regular Sasakian-Einstein
orbifolds to the general quasi-regular Sasakian case. This allows for the further construction of specific types of Sasakian
structures that are preserved under the join operation, such as positive, negative, or null Sasakian structures, as well as
Sasakian-Einstein structures. In particular, we show that there are families of Sasakian-Einstein structures on certain 7-manifolds
homeomorphic to S
2 × S
5. We next show how the join construction emerges as a special case of Lerman’s contact fibre bundle construction [32]. In
particular, when both the base and the fiber of the contact fiber bundle are toric we show that the construction yields a
new toric Sasakian manifold. Finally, we study toric Sasakian manifolds in dimension 5 and show that any simply-connected
compact oriented 5-manifold with vanishing torsion admits regular toric Sasakian structures. This is accomplished by explicitly
constructing circle bundles over the equivariant blow-ups of Hirzebruch surfaces.
During the preparation of this work the first two authors were partially supported by NSF grants DMS-0203219 and DMS-0504367. 相似文献
4.
Henrik Pedersen Yat Sun Poon 《Proceedings of the American Mathematical Society》1999,127(10):3027-3034
Making use of the relations among 3-Sasakian manifolds, hypercomplex manifolds and quaternionic Kähler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.
5.
A Sasakian structure
=(\xi,\eta,\Phi,g) on a manifold Mis called positiveif its basic first Chern class c1(
) can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This provides us with a new technique for proving the existence of positive Ricci curvature metrics on certain odd dimensional manifolds. As an example we give a completely independent proof of a result of Sha and Yang that for every nonnegative integer kthe 5-manifolds k#(S
2×S
3) admits metrics of positive Ricci curvature. 相似文献
6.
We consider classes of weakly cosymplectic manifolds whose Riemannian curvature tensors satisfy contact analogs of the Riemannian–Christoffel
identities. Additional properties of the Riemannian curvature tensor symmetry are found and a classification of weakly cosymplectic
manifolds is obtained. 相似文献
7.
8.
M. Tarafdar 《Periodica Mathematica Hungarica》1991,22(2):125-128
9.
S. V. Kharitonova 《Mathematical Notes》2009,86(1-2):121-131
We obtain the complete group of structure equations of a locally conformally almost cosymplectic structure (an lc $ ACy $ -structure in what follows) and compute the components of the Riemannian curvature tensor on the space of the associated G-structure. Normal lc $ ACy $ -structures are studied in more detail. In particular, we prove that the contact analogs of A. Gray’s second and third curvature identities hold on normal lc $ ACy $ -manifolds, while the contact analog of A. Gray’s first identity holds if and only if the manifold is cosymplectic. 相似文献
10.
Normal locally conformal almost cosymplectic structures (or -structures) are considered. A full set of structure equations is obtained, and the components of the Riemannian curvature tensor and the Ricci tensor are calculated. Necessary and sufficient conditions for the constancy of the curvature of such manifolds are found. In particular, it is shown that a normal -manifold which is a spatial form has nonpositive curvature. The constancy of ΦHS-curvature is studied. Expressions for the components of the Weyl tensor on the space of the associated G-structure are obtained. Necessary and sufficient conditions for a normal -manifold to coincide with the conformal plane are found. Finally, locally symmetric normal -manifolds are considered. 相似文献
11.
A contact manifold M can be defined as a quotient of a symplectic manifold X by a proper, free action of \(\mathbb{R}\), with the symplectic form homogeneous of degree 2. If X is also Kähler, and its metric is homogeneous of degree 2, M is called Sasakian. A Sasakian manifold is realized naturally as a level set of a Kähler potential on a complex manifold, hence it is equipped with a pseudoconvex CR-structure. We show that any Sasakian manifold M is CR-diffeomorphic to an S 1-bundle of unit vectors in a positive line bundle on a projective Kähler orbifold. This induces an embedding of M into an algebraic cone C. We show that this embedding is uniquely defined by the CR-structure. Additionally, we classify the Sasakian metrics on an odd-dimensional sphere equipped with a standard CR-structure. 相似文献
12.
13.
Hiroshi Endo 《Journal of Geometry》2012,103(2):231-236
We shall show that the first Betti number of some class of compact nearly cosymplectic manifolds is zero or even. 相似文献
14.
SkewCRSubmanifoldsofaSasakianManifoldLiuXimin(刘西民)(DepartmentofMathematics,NankaiUniversity,Tianjin,300071)LiangXiquan(梁希泉)(I... 相似文献
15.
本文讨论了Sasaki 几何中的能量泛函Ek, 推导出其Euler-Lagrange 方程, 进而证明其临界度量的唯一性定理. 另外, 我们得到了具有常横截σk 曲率的Sasaki 度量的唯一性结论. 相似文献
16.
Liu Ximin 《Proceedings Mathematical Sciences》2001,111(4):399-405
LetM
n be a Riemanniann-manifold. Denote byS(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature onM
n, respectively. In this paper we prove that everyC-totally real submanifold of a Sasakian space formM
2m+1(c) satisfies
, whereH
2 andg are the square mean curvature function and metric tensor onM
n, respectively. The equality holds identically if and only if eitherM
n is totally geodesic submanifold or n = 2 andM
n is totally umbilical submanifold. Also we show that if aC-totally real submanifoldM
n ofM
2n+1 (c) satisfies
identically, then it is minimal. 相似文献
17.
On the basis of the so-called phase completion the notion of vertical, horizontal and complete objects is defined in the tangent
bundles over Finslerian and Riemannian manifold. Such a tangent bundle is made into a manifold of almost Kaehlerian structure
by endowing it with Sasakian metric. The components of curvature tensors with respect to the adapted frame are presented.
This having been done it is shown possible to study the differential geometry of Finslerian spaces by dealing with that of
their own tangent bundles.
This work was supported by National Research Coundil of Canada A-4037 (1960–70).
Entrata in Redazione l'8 marzo 1970. 相似文献
18.
Semi-Slant Submanifolds of a Sasakian Manifold 总被引:1,自引:0,他引:1
We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold. We prove a characterization theorem for semi-slant submanifolds and we obtain integrability conditions for the distributions which are involved in the definition of such submanifolds. We also study an interesting particular class of semi-slant submanifolds. 相似文献
19.
20.
We investigate the curvature properties of a two-parameter family of Hermitian structures on the product of two Sasakian manifolds, as well as intermediate relations. We give a necessary and sufficient condition for a Hermitian structure belonging to the family to be Einstein and provide concrete examples. 相似文献