A contact metric manifold satisfying a certain curvature condition

Jong Taek Cho

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 4, page 319-333
  • ISSN: 0044-8753

Abstract

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In the present paper we investigate a contact metric manifold satisfying (C) ( ∇ ¯ γ ˙ R ) ( · , γ ˙ ) γ ˙ = 0 for any ∇ ¯ -geodesic γ , where ∇ ¯ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any ∇ ¯ -geodesic γ . Also, we prove a structure theorem for a contact metric manifold with ξ belonging to the k -nullity distribution and satisfying (C) for any ∇ ¯ -geodesic γ .

How to cite

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Cho, Jong Taek. "A contact metric manifold satisfying a certain curvature condition." Archivum Mathematicum 031.4 (1995): 319-333. <http://eudml.org/doc/247685>.

@article{Cho1995,
abstract = {In the present paper we investigate a contact metric manifold satisfying (C) $(\bar\{\nabla \}_\{\dot\{\gamma \}\}R)(\cdot ,\dot\{\gamma \})\dot\{\gamma \}=0$ for any $\bar\{\nabla \}$-geodesic $\gamma $, where $\bar\{\nabla \}$ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any $\bar\{\nabla \}$-geodesic $\gamma $. Also, we prove a structure theorem for a contact metric manifold with $\xi $ belonging to the $k$-nullity distribution and satisfying (C) for any $\bar\{\nabla \}$-geodesic $\gamma $.},
author = {Cho, Jong Taek},
journal = {Archivum Mathematicum},
keywords = {contact metric manifolds; Tanaka connection; Jacobi operator; Jacobi operator; contact metric manifold; locally -symmetric space; constant sectional curvature},
language = {eng},
number = {4},
pages = {319-333},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A contact metric manifold satisfying a certain curvature condition},
url = {http://eudml.org/doc/247685},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Cho, Jong Taek
TI - A contact metric manifold satisfying a certain curvature condition
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 4
SP - 319
EP - 333
AB - In the present paper we investigate a contact metric manifold satisfying (C) $(\bar{\nabla }_{\dot{\gamma }}R)(\cdot ,\dot{\gamma })\dot{\gamma }=0$ for any $\bar{\nabla }$-geodesic $\gamma $, where $\bar{\nabla }$ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma $. Also, we prove a structure theorem for a contact metric manifold with $\xi $ belonging to the $k$-nullity distribution and satisfying (C) for any $\bar{\nabla }$-geodesic $\gamma $.
LA - eng
KW - contact metric manifolds; Tanaka connection; Jacobi operator; Jacobi operator; contact metric manifold; locally -symmetric space; constant sectional curvature
UR - http://eudml.org/doc/247685
ER -

References

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  13. Ricci curvature of contact Riemannian manifolds, Tôhoku Math. J. 40 (1988), 441-448. (1988) MR0957055
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