共查询到20条相似文献,搜索用时 0 毫秒
1.
In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed
to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct
the first known examples of harmonic morphisms from the non-compact Lie groups , SU
*(2n), , SO
*(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics.
相似文献
2.
We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups SLn(R), SU∗(2n) and Sp(n,R) equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO∗(2n), SO(p,q), SU(p,q) and Sp(p,q). Applying a duality principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics. 相似文献
3.
Sigmundur Gudmundsson Martin Svensson 《Differential Geometry and its Applications》2006,24(4):351-366
In this paper we prove the local existence of complex-valued harmonic morphisms from any compact semisimple Lie group and their non-compact duals. These include all Riemannian symmetric spaces of types II and IV. We produce a variety of concrete harmonic morphisms from the classical compact simple Lie groups SO(n), SU(n), Sp(n) and globally defined solutions on their non-compact duals SO(n,C)/SO(n), SLn(C)/SU(n) and Sp(n,C)/Sp(n). 相似文献
4.
Jonas Nordström 《Annals of Global Analysis and Geometry》2014,45(1):1-10
We study left-invariant complex-valued harmonic morphisms from Riemannian Lie groups. We show that in each dimension greater than 3 there exist Riemannian Lie groups that do not have any such solutions. 相似文献
5.
Nazih Nahlus 《Proceedings of the American Mathematical Society》2003,131(5):1321-1327
Let be an algebraically closed field of arbitrary characteristic, and let be a surjective morphism of connected pro-affine algebraic groups over . We show that if is bijective and separable, then is an isomorphism of pro-affine algebraic groups. Moreover, is separable if and only if (its differential) is surjective. Furthermore, if is separable, then .
6.
7.
Scott Van Thuong 《Annals of Global Analysis and Geometry》2017,51(2):109-128
We classify left invariant metrics on the 4-dimensional, simply connected, unimodular Lie groups up to automorphism. When the corresponding Lie algebra is of type (R), this is equivalent to classifying the left invariant metrics up to isometry, but in general the classification up to automorphism is finer than that up to isometry. In the abelian case, all left invariant metrics are isometric. In the nilpotent case, the space of metrics can have dimension 1 or 3. In the solvable case, the dimension can be 2, 4, or 5. There are two non-solvable 4-dimensional unimodular groups, and the space of metrics has dimension 6 in both of these cases. 相似文献
8.
Sigmundur Gudmundsson 《Geometriae Dedicata》1994,53(2):155-161
In this paper we study harmonic morphisms :U P
m N
2 from open subsets of complex projective spaces to Riemann surfaces. We construct many new examples of such maps which are not holomorphic with respect to the standard Kähler structure on P
m.The research leading to this paper was supported by the Icelandic Science Fund and the Danish National Science Fund. 相似文献
9.
Sigmundur Gudmundsson 《Geometriae Dedicata》1995,56(3):327-332
In this paper we give a method for constructing harmonic morphisms from quaternionic projective spaces P
k with values in a Riemann surface.The research leading to this paper was partially done at the Mathematics Institute of the University of Copenhagen and supported by the Danish Science Research Council. 相似文献
10.
We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This
yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing
left-invariant foliations on a large class of Lie groups producing harmonic morphisms. 相似文献
11.
Anna Fino 《manuscripta mathematica》2002,109(4):527-541
We study geometrical structures on the cotangent bundle T
*
G of a Lie group G which are left-invariant with respect to the Lie group structure on T
*
G determined by a left-invariant affine structure ∇ on G. In particular, we investigate the existence of conformally hyper-K?hler metrics and hyper-K?hler with torsion (HKT) structures
on the cotangent bundle of hypercomplex 4-dimensional Lie groups. By applying In?nü-Wigner contractions to compact semisimple
Lie algebras we obtain non semisimple Lie algebras endowed with invariant HKT structures.
Received: 4 February 2002 / Revised version: 20 August 2002
Research partially supported by MURST and GNSAGA (Indam) of Italy
Mathematics Subject Classification (2000): 53C26, 22E25 相似文献
12.
Kensuke Onda 《Geometriae Dedicata》2010,147(1):313-322
The three-dimensional Heisenberg group H
3 has three left-invariant Lorentzian metrics g
1, g
2, and g
3 as in Rahmani (J. Geom. Phys. 9(3), 295–302 (1992)). They are not isometric to each other. In this paper, we characterize
the left-invariant Lorentzian metric g
1 as a Lorentz Ricci Soliton. This Ricci Soliton g
1 is a shrinking non-gradient Ricci Soliton. We also prove that the group E(2) of rigid motions of Euclidean 2-space and the group E(1, 1) of rigid motions of Minkowski 2-space have Lorentz Ricci Solitons. 相似文献
13.
14.
Barbara Priwitzer 《Geometriae Dedicata》1994,52(1):33-40
We prove the following theorem: LetP be an 8-dimensional compact topological projective plane. If the connected component of its automorphism group has dimension at least 12, then is a Lie group. 相似文献
15.
16.
Armen Glebovich Sergeev 《中国科学A辑(英文版)》2008,51(4):695-706
We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ1 into ΩG are related to Yang-Mills G-fields on ℝ4.
This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific
Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics” 相似文献
17.
J. C. Wood 《Journal of Mathematical Sciences》1999,94(2):1263-1269
A harmonic morphism is a map between Riemannian manifolds which preserves Laplace's equation. We compare the properties of
harmonic morphisms with those of the better known harmonic maps, seeing that they behave in some ways “dual” to the latter.
In particular, we give representation theorems for harmonic morphisms in low dimensions which suggest that the equations might
be soluble in some cases by integrable-system techniques in a similar way to that used in harmonic map theory. Bibliography:
38 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 190–200. 相似文献
18.
We prove that any (real or complex) analytic horizontally conformalsubmersion from a three-dimensional conformal manifold (M3,cM) to a two-dimensional conformal manifold (N2, cN) can be,locally, extended to a unique harmonic morphismfrom the (eaven)-space (H4, g) of (M3, cN) to (N2, cN). Moreover,any positive harmonic morphism with two-dimensional fibres from(H4, g) is obtained in this way. 相似文献
19.
A. G. Sergeev 《Journal of Mathematical Sciences》2008,149(5):1608-1617
We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. Harmonic maps into loop spaces are of special interest because of their relation to the Yang-Mills
equations on ℝ4.
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 16, Differential and Functional Differential Equations. Part 2, 2006. 相似文献
20.
In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases.
Mathematics Subject Classifications (2000): 58E20, 53C43, 53C12The author is a member of EDGE, Research Training Network HPRN-CT-2000-00101 相似文献