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Keywords:
contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation
contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation
Summary:
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 $.
References:
[1] Baikoussis C., Koufogiorgos T.: On a type of contact manifolds. to appear in Journal of Geometry. MR 1205692
[2] Blair D.E.: Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1979. MR 0467588 | Zbl 0319.53026
[3] Blair D.E.: Two remarks on contact metric structures. Tôhoku Math. J. 29 (1977), 319-324. MR 0464108 | Zbl 0376.53021
[4] Blair D.E., Koufogiorgos T., Papantoniou B.J.: Contact metric manifolds with characteristic vector field satisfying $R(X,Y)\xi =k(\eta (Y)X-\eta (X)Y)+\mu (\eta (Y)hX-\eta (X)hY)$. 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. MR 1201408
[7] Tanno S.: Ricci curvatures of contact Riemannian manifolds. Tôhoku Math J. 40 (1988), 441-448. MR 0957055 | Zbl 0655.53035
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