• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.149-164
• /
• 2021

By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.327-340
• /
• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• Korean Journal of Childcare and Education
• /
• v.15 no.3
• /
• pp.83-113
• /
• 2019

Objective: This study aimed to develop and apply the home connection program for promoting the mathematical interaction of parents of 3-year-olds. Methods: We surveyed questionnaires for 36 parents and interviewed 3 parents of 3-year-olds for the development of the program. Twenty-one 3-year-olds were selected as participants in the program. Quantitative data from a checklist for parent's mathematical interaction were analyzed using repeated measures ANOVA. Qualitative data from self-evaluation of teachers and parents were categorized and analyzed in terms of meaning. Results: Based on the home connection program, the session were provided in the following order [educare center activities ${\rightarrow}$ home-linked activities ${\rightarrow}$ home+educare integrated activities] and in each session, the three-step course [sharing of thinking ${\rightarrow}$ gathering of thinking ${\rightarrow}$ broadening of thinking] was applied. Implementation of this program led to promoting parental mathematical interaction. Conclusion/Implications: This study will lead to follow-up studies that reveal positive effects of our program.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.843-852
• /
• 2013

The characteristic connection is a good substitute for Levi-Civita connection in studying non-integrable geometries. In this paper we consider the homogeneous space $U(3)/(U(1){\times}U(1){\times}U(1))$ with a one-parameter family of Hermitian structures. We prove that the one-parameter family of Hermtian structures admit a characteristic connection. We also compute the torsion of the characteristic connecitons.

• East Asian mathematical journal
• /
• v.33 no.5
• /
• pp.543-557
• /
• 2017

Jin [10] studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. We study further the geometry of this subject. The object of this paper is to study the geometry of half lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection.

• Kyungpook Mathematical Journal
• /
• v.56 no.4
• /
• pp.1237-1246
• /
• 2016

In this paper we study some properties of submanifolds of a Riemannian manifold equipped with a generalized connection $\hat{\nabla}$. We also consider almost Hermitian manifolds that admits a special case of this generalized connection and derive some results about the behavior of this manifolds.

• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.119-133
• /
• 2017

In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.3
• /
• pp.477-487
• /
• 2009

We define a quarter symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider invariant, noninvariant and anti-invariant hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection.

• Communications of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.979-998
• /
• 2020

We study totally umbilical real half lightlike submanifolds of indefinite Kaehler manifolds with a quarter-symmetric metric connection. We obtain some conditions for a real half lightlike submanifold of an indefinite Kaehler manifold with a quarter-symmetric metric connection to be a product manifold. We derive the expression for induced Ricci type tensor 𝓡^(0,2) and also obtain conditions for 𝓡^(0,2) to be symmetric.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.895-903
• /
• 2009

We define a semi-symmetric metric connection in an almost $\gamma$-paracontact Riemannian manifold and we consider invariant, non-invariant and anti-invariant hypersurfaces of an almost $\gamma$-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.