Contact manifolds, harmonic curvature tensor and ( k , μ ) -nullity distribution

Basil J. Papantoniou

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 323-334
  • ISSN: 0010-2628

Abstract

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In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field ξ belongs to the ( k , μ ) -nullity distribution. Next it is shown that the dimension of the ( k , μ ) -nullity distribution is equal to one and therefore is spanned by the characteristic vector field ξ .

How to cite

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Papantoniou, Basil J.. "Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 323-334. <http://eudml.org/doc/247482>.

@article{Papantoniou1993,
abstract = {In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field $\xi $ belongs to the $(k,\mu )$-nullity distribution. Next it is shown that the dimension of the $(k,\mu )$-nullity distribution is equal to one and therefore is spanned by the characteristic vector field $\xi $.},
author = {Papantoniou, Basil J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation; contact Riemannian manifold; harmonic curvature; -homothetic deformation},
language = {eng},
number = {2},
pages = {323-334},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution},
url = {http://eudml.org/doc/247482},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Papantoniou, Basil J.
TI - Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 323
EP - 334
AB - In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field $\xi $ belongs to the $(k,\mu )$-nullity distribution. Next it is shown that the dimension of the $(k,\mu )$-nullity distribution is equal to one and therefore is spanned by the characteristic vector field $\xi $.
LA - eng
KW - contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation; contact Riemannian manifold; harmonic curvature; -homothetic deformation
UR - http://eudml.org/doc/247482
ER -

References

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  1. Baikoussis C., Koufogiorgos T., On a type of contact manifolds, to appear in Journal of Geometry. MR1205692
  2. Blair D.E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1979. Zbl0319.53026MR0467588
  3. Blair D.E., Two remarks on contact metric structures, Tôhoku Math. J. 29 (1977), 319-324. (1977) Zbl0376.53021MR0464108
  4. Blair D.E., Koufogiorgos T., Papantoniou B.J., Contact metric manifolds with characteristic vector field satisfying R ( X , Y ) ξ = k ( η ( Y ) X - η ( X ) Y ) + μ ( η ( Y ) h X - η ( X ) h Y ) , submitted. 
  5. Deng S.R., Variational problems on contact manifolds, Thesis, Michigan State University, 1991. 
  6. Koufogiorgos T., Contact metric manifolds, to appear in Annals of Global Analysis and Geometry. MR1201408
  7. Tanno S., Ricci curvatures of contact Riemannian manifolds, Tôhoku Math J. 40 (1988), 441-448. (1988) Zbl0655.53035MR0957055

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