Infinitesimal characterization of almost Hermitian homogeneous spaces

Sergio Console; Lorenzo Nicolodi

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 4, page 713-721
  • ISSN: 0010-2628

Abstract

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In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer k H , the covariant derivatives of the curvature tensor up to order k H + 2 and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given.

How to cite

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Console, Sergio, and Nicolodi, Lorenzo. "Infinitesimal characterization of almost Hermitian homogeneous spaces." Commentationes Mathematicae Universitatis Carolinae 40.4 (1999): 713-721. <http://eudml.org/doc/248425>.

@article{Console1999,
abstract = {In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer $k_H$, the covariant derivatives of the curvature tensor up to order $k_H+2$ and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given.},
author = {Console, Sergio, Nicolodi, Lorenzo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {almost Hermitian homogeneous spaces; Singer invariant; almost Hermitian homogeneous space; Singer invariant; almost Hermitian infinitesimal model},
language = {eng},
number = {4},
pages = {713-721},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Infinitesimal characterization of almost Hermitian homogeneous spaces},
url = {http://eudml.org/doc/248425},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Console, Sergio
AU - Nicolodi, Lorenzo
TI - Infinitesimal characterization of almost Hermitian homogeneous spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 4
SP - 713
EP - 721
AB - In this note it is shown that almost Hermitian locally homogeneous manifolds are determined, up to local isometries, by an integer $k_H$, the covariant derivatives of the curvature tensor up to order $k_H+2$ and the covariant derivatives of the complex structure up to the second order calculated at some point. An example of a Hermitian locally homogeneous manifold which is not locally isometric to any Hermitian globally homogeneous manifold is given.
LA - eng
KW - almost Hermitian homogeneous spaces; Singer invariant; almost Hermitian homogeneous space; Singer invariant; almost Hermitian infinitesimal model
UR - http://eudml.org/doc/248425
ER -

References

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  2. Kowalski O., Generalized Symmetric Spaces, Lecture Notes in Math. 805 Springer Berlin (1980). (1980) Zbl0431.53042MR0579184
  3. Kowalski O., Counter-example to the ``Second Singer's Theorem'', Ann. Global Anal. Geom. 8 (1990), 211-214. (1990) Zbl0736.53047MR1088512
  4. Kowalski O., Tricerri F., A canonical connection for locally homogeneous Riemannian manifolds, D. Ferus et al. Proc. Conf. Global Diff. Geom. and Global Analysis, Berlin, 1990, Lecture Notes in Math. 1481 Springer Berlin (1990), 97-103. (1990) MR1178522
  5. Lastaria F., Tricerri F., Curvature orbits and locally homogeneous Riemannian manifolds, Ann. Mat. Pura Appl. 165 (1993), 121-131. (1993) Zbl0804.53072MR1271415
  6. Nomizu K., Invariant affine connections on homogeneous spaces, Amer. J. Math. 76 (1954), 33-65. (1954) Zbl0059.15805MR0059050
  7. Nicolodi L., Tricerri F., On two theorems of I.M. Singer about homogeneous spaces, Ann. Global Anal. Geom. 8 (1990), 193-209. (1990) Zbl0676.53058MR1088511
  8. Sekigawa K., Notes on homogeneous almost Hermitian manifolds, Hokkaido Math. J. 7 (1978), 206-213. (1978) Zbl0388.53014MR0509406
  9. Singer I.M., Infinitesimally homogeneous spaces, Comm. Pure Appl. Math. 13 (1960), 685-697. (1960) Zbl0171.42503MR0131248
  10. Tricerri F., Locally homogeneous Riemannian manifolds, Rend. Sem. Mat. Univ. Politec. Torino 50/4 (1993), 411-426. (1993) Zbl0804.53072MR1261452
  11. Tricerri F., Vanhecke L., Homogeneous Structures on Riemannian Manifolds, London Mathematical Society Lecture Notes Series 83, Cambridge University Press Cambridge (1983). (1983) Zbl0509.53043MR0712664
  12. Tricerri F., Watanabe Y., Infinitesimal models and locally homogeneous almost Hermitian manifolds, Math. J. Toyama Univ. 18 (1995), 147-154. (1995) Zbl0865.53042MR1369702

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