• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.229-241
• /
• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.3
• /
• pp.281-293
• /
• 2019

In the present paper, we study quasi-concircular curvature tensor satisfying certain curvature conditions on a Lorentzian ${\beta}$-Kenmotsu manifold with respect to the semi-symmetric semi-metric connection.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.339-359
• /
• 2022

In this paper, we investigate k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using this curvatures, we establish some inequalities for screen homothetic lightlike hypersurface of a real space form ${\tilde{M}}$(c) of constant sectional curvature c, endowed with semi-symmetric non-metric connection. Using these inequalities, we obtain some characterizations for such hypersurfaces. Considering the equality case, we obtain some results.

• Korean Journal of Mathematics
• /
• v.8 no.1
• /
• pp.53-61
• /
• 2000

The object of this paper is to find the 4-dimensional compact Einstein manifold with negative Ricci curvature $r$.

• Communications of the Korean Mathematical Society
• /
• v.8 no.4
• /
• pp.689-697
• /
• 1993

• Journal of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.55-60
• /
• 1982

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.177-186
• /
• 2017

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.331-340
• /
• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.273-278
• /
• 2012

Using a comparison of the Jacobi differential equations instead of volume comparison by Itokawa in [3], the focal radius is estimated under the suitable Ricci and mean curvature conditions.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1189-1208
• /
• 2017

In this paper, we study vanishing properties for $L^2$ harmonic 1-forms on a gradient shrinking Ricci soliton. We prove that if (M, g, f) is a complete oriented noncompact gradient shrinking Ricci soliton with potential function f, then there are no non-trivial $L^2$ harmonic 1-forms which are orthogonal to df. Second, we show that if the scalar curvature of the metric g is greater than or equal to (n - 2)/2, then there are no non-trivial $L^2$ harmonic 1-forms on (M, g). We also show that any multiplication of the total differential df by a function cannot be an $L^2$ harmonic 1-form unless it is trivial. Finally, we derive various integral properties involving the potential function f and $L^2$ harmonic 1-forms, and handle their applications.