CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions

Fumio Narita

Colloquium Mathematicae (1996)

  • Volume: 70, Issue: 2, page 165-179
  • ISSN: 0010-1354

Abstract

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We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.

How to cite

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Narita, Fumio. "CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions." Colloquium Mathematicae 70.2 (1996): 165-179. <http://eudml.org/doc/210403>.

@article{Narita1996,
abstract = {We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.},
author = {Narita, Fumio},
journal = {Colloquium Mathematicae},
keywords = {holomorphic sectional curvature; strictly locally conformal Kähler manifold; CR-submanifold; Riemannian submersion},
language = {eng},
number = {2},
pages = {165-179},
title = {CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions},
url = {http://eudml.org/doc/210403},
volume = {70},
year = {1996},
}

TY - JOUR
AU - Narita, Fumio
TI - CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions
JO - Colloquium Mathematicae
PY - 1996
VL - 70
IS - 2
SP - 165
EP - 179
AB - We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.
LA - eng
KW - holomorphic sectional curvature; strictly locally conformal Kähler manifold; CR-submanifold; Riemannian submersion
UR - http://eudml.org/doc/210403
ER -

References

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  17. [17] I. Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. 12 (1979), 263-284. Zbl0447.53032
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