arXiv subjects

Ken'ichi Sekiya

Publications and source records attributed to Ken'ichi Sekiya.

3 recordsLinked to original sources

arXiv2012

Generalized almost contact structures and generalized Sasakian structures

We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact structures. We obtain a generalized Sasakian structure on a non-compact manifold which does not arise as a pair of ordinary Sasakian structures. However we show that a generalized Sasakian structure on compact 3-dimensional manifold is equivalent to a pair of Sasakian structures with the same metric. Finally we extend a definition of a generalized almost contact structure.

math.DG↗

arXiv2009

A diameter bound for Sasaki manifolds with application to uniqueness for Sasaki-Einstein structure

In this paper we give a diameter bound for Sasaki manifolds with positive transverse Ricci curvature. As an application, we obtain the uniqueness of Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure.

math.DG↗

arXiv2009

On the uniqueness of Sasaki-Einstein metrics

Let $S$ be a compact Sasakian manifold which does not admit non-trivial Hamiltonian holomorphic vector fields. If there exists an Einstein-Sasakian metric on $S$, then it is unique.

math.DG↗