• East Asian mathematical journal
• /
• 제33권5호
• /
• pp.533-542
• /
• 2017

We study the geometry of indefinite trans-Sasakian manifold ${\bar{M}}$ admitting a half lightlike submanifold M such that the structure vector field of ${\bar{M}}$ belongs to the transversal vector bundle of M. We prove several classification theorems of such an indefinite trans-Sasakian manifold.

• 호남수학학술지
• /
• 제35권4호
• /
• pp.657-666
• /
• 2013

We study indefinite trans-Sasakian manifold $\bar{M}$ admitting an ascreen lightlike hypersurface M. Our main results are several classification theorems of such an indefinite trans-Sasakian manifold.

• 호남수학학술지
• /
• 제45권2호
• /
• pp.215-230
• /
• 2023

In this article, generalized Sasakian space forms are investigated on W₀ -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W₀-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W₀-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W₀-pseudosymmetry and W₀ -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

• 대한수학회논문집
• /
• 제13권2호
• /
• pp.337-343
• /
• 1998

In this paper we show that every contact metric manifold with vanishing contact conformal curvature tensor is a Sasakian space form.

• 대한수학회보
• /
• 제40권1호
• /
• pp.63-76
• /
• 2003

In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

• 대한수학회논문집
• /
• 제9권2호
• /
• pp.401-409
• /
• 1994

One of typical submanifolds of a Sasakian manifold is the so-called generic submanifolds which are defined as follows: Let M be a submanifold of a Sasakian manifold M with almost contact metric structure (ø, G, ξ) such that M is tangent to the structure vector ξ. If each normal space is mapped into the tangent space under the action of ø, M is called a generic submanifold of M [2], [8].(omitted)

• 대한수학회지
• /
• 제43권5호
• /
• pp.1019-1045
• /
• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• 대한수학회논문집
• /
• 제29권3호
• /
• pp.451-461
• /
• 2014

We study the geometry of indefinite trans-Sasakian manifold $\bar{M}$, of type (${\alpha},{\beta}$), admitting a half lightlike submanifold M such that the structure vector field of $\bar{M}$ does not belong to the screen and coscreen distributions of M. The purpose of this paper is to prove several classification theorems of such an indefinite trans-Sasakian manifold.

• 대한수학회논문집
• /
• 제31권3호
• /
• pp.613-624
• /
• 2016

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (${\ell}$, m).

• Korean Journal of Mathematics
• /
• 제10권2호
• /
• pp.157-166
• /
• 2002

We show that the contact conformal curvature tensor on 3-dimensional Sasakian manifold always vanishes. We also prove that if the contact conformal curvature tensor vanishes on a 3-dimensional locally ${\varphi}$-symmetric contact metric manifold M, then M is a Sasakian space form.