On Cauchy-Riemann submanifolds whose local geodesic symmetries preserve the fundamental form

Sorin Dragomir; Mauro Capursi

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 99-103
  • ISSN: 0066-2216

Abstract

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We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.

How to cite

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Sorin Dragomir, and Mauro Capursi. "On Cauchy-Riemann submanifolds whose local geodesic symmetries preserve the fundamental form." Annales Polonici Mathematici 57.2 (1992): 99-103. <http://eudml.org/doc/262310>.

@article{SorinDragomir1992,
abstract = {We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.},
author = {Sorin Dragomir, Mauro Capursi},
journal = {Annales Polonici Mathematici},
keywords = {Cauchy-Riemann submanifolds; Riemannian product; totally geodesic complex submanifold; totally real submanifold},
language = {eng},
number = {2},
pages = {99-103},
title = {On Cauchy-Riemann submanifolds whose local geodesic symmetries preserve the fundamental form},
url = {http://eudml.org/doc/262310},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Sorin Dragomir
AU - Mauro Capursi
TI - On Cauchy-Riemann submanifolds whose local geodesic symmetries preserve the fundamental form
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 99
EP - 103
AB - We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.
LA - eng
KW - Cauchy-Riemann submanifolds; Riemannian product; totally geodesic complex submanifold; totally real submanifold
UR - http://eudml.org/doc/262310
ER -

References

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  1. [1] B. Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Agnew. Math. 325 (1981), 28-67. Zbl0503.53013
  2. [2] S. Dragomir, Cauchy-Riemann submanifolds of locally conformal Kaehler manifolds, I, II, Geom. Dedicata 28 (1988), 181-197; Atti Sem. Mat. Fis. Univ. Modena 37 (1989), 1-11. Zbl0659.53041
  3. [3] S. Dragomir, On submanifolds of Hopf manifolds, Israel J. Math. (2) 61 (1988), 199-210. Zbl0649.53031
  4. [4] A. Gray, The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J. 20 (1973), 329-344. Zbl0279.58003
  5. [5] K. Sekigawa and L. Vanhecke, Symplectic geodesic symmetries on Kaehler manifolds, Quart. J. Math. Oxford Ser. (2) 37 (1986), 95-103. Zbl0589.53068
  6. [6] I. Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. 12 (1979), 263-284. Zbl0447.53032
  7. [7] K. Yano, On a structure defined by a tensor field of type (1,1) satisfying f³+f=0, Tensor (N.S.) 14 (1963), 99-109. Zbl0122.40705
  8. [8] K. Yano and M. Kon, Generic submanifolds, Ann. Mat. Pura Appl. 123 (1980), 59-92. Zbl0441.53043
  9. [9] K. Yano and M. Kon, Cr Submanifolds of Kaehlerian and Sasakian Manifolds, Progr. Math. 30, Birkhäuser, Boston 1983. Zbl0496.53037

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