• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.457-464
• /
• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.863-881
• /
• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.235-243
• /
• 2010

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter symmetric connections, even some of them are not introduced so far. So, in this paper, we define a quarter symmetric semi-metric connection in an almost r-paracontact Riemannian manifold and consider invariant, non-invariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold with that connection.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.689-700
• /
• 2008

In this paper we prove that a $\phi$-recurrent (k, $\mu$)-contact metric manifold is an $\eta$-Einstein manifold with constant coefficients. Next, we prove that a three-dimensional locally $\phi$-recurrent (k, $\mu$)-contact metric manifold is the space of constant curvature. The existence of $\phi$-recurrent (k, $\mu$)-manifold is proved by a non-trivial example.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.321-327
• /
• 1999

Graves and Nomizu investigated an indefinite version of the Cartan's result. Specifically they obtained the conditions for all non-degenerate planes to have the same sectional curvature in the in-definite Riemannian manifold. In this paper we are to study the cosym-plective version of the results of Graves and Nomizu and characterize an indefinite cosymplectic spce form.

• Communications of the Korean Mathematical Society
• /
• v.15 no.4
• /
• pp.641-648
• /
• 2000

The purpose of this paper is to give a necessary and sufficient condition for a smooth manifold to admit a Lorentzian metric. As an application of this result, on Lorentzian manifolds we have shown that the existence of a 1-dimensional distribution is equivalent to the existence of a non-vanishing vector field.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1996.11a
• /
• pp.578-582
• /
• 1996

Verification of STL is essential in RP. In the study, triangle based non-manifold geometric modeling that can check intersection between triangles was used to vilify STL. The method proposed in this study can be applied at the most general case and very useful, but has a penalty on computing thime of O(n$^2$)

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.865-879
• /
• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• Communications of the Korean Mathematical Society
• /
• v.23 no.3
• /
• pp.413-420
• /
• 2008

The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.

• Communications of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.921-934
• /
• 2019

The object of the present paper is to study generalized pseudo-projectively symmetric manifolds and Einstein generalized pseudo-projectively symmetric manifolds. Finally, the existence of generalized pseudo-projectively symmetric manifolds have been proved by two non-trivial examples.