# On indefinite η-Einstein Sasakian manifold

18 Apr 2012-Lobachevskii Journal of Mathematics (SP MAIK Nauka/Interperiodica)-Vol. 33, Iss: 1, pp 28-32

TL;DR: In this article, the authors have studied the properties of indefinite η-Einstein Sasakian manifold and introduced an example of a SISKIAN manifold with an example.

Abstract: This present paper is to study on indefinite η-Einstein Sasakian manifold which is introduced with an example. Here some properties of indefinite η-Einstein Sasakian manifold have been studied.

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01 Jan 1976

TL;DR: In this paper, the tangent sphere bundle is shown to be a contact manifold, and the contact condition is interpreted in terms of contact condition and k-contact and sasakian structures.

Abstract: Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.

1,259 citations

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331 citations

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Nihon University

^{1}TL;DR: In this article, the authors studied the problem of finding a (φ, ξ, η, g)-connection in a space with a normal contact structure and proved that the space with such a contact structure is an Einstein space.

Abstract: Introduction. Recently S. Sasaki [3]° defined the notion of (φ, ξ, η, g) structure of a differentiable manifold. Further, S. Sasaki and Y. Hatakeyama [ 4 ] [ 5 ] showed that the structure is closely related to contact structure. By means of this notion, it is shown that a space with a contact structure can be dealt with as we deal with an almost complex space. So, by similar manner, some problems discussed in the latter space may be considered in the former. On the other hand, S. Tachibana [6] [7] proved many interesting theorems in an almost complex space. In this paper, the present author tries to study, in the space with a certain contact structure, the problem corresponding to S. Tachibana's results. We shall devote § 1 to preliminaries and in this section introduce a normal contact structure. In §2, we ennumerate identities which will be useful in the later sections. We shall prove in § 3 that a space with a normal contact structure satisfying VkRjt = 0 be necessarily an Einstein one and that a symmetric space with a normal contact structure reduces to the space of constant curvature respectively. The differential form R is dealt with in § 4, and in this section, we shall show a necessary and sufficient condition that the space be an Einstein space by means of the form R. Finally in § 5, we introduce a certain type of (φ, η,

178 citations

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...Okumura in 1962 [8]....

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