• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.41-63
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• 2024

In this paper, we study complete Riemannian immersions into a semi-Riemannian warped product obeying suitable curvature constraints. Under appropriate differential inequalities involving higher order mean curvatures, we establish rigidity and nonexistence results concerning these immersions. Applications to the cases that the ambient space is either an Einstein manifold, a steady state type spacetime or a pseudo-hyperbolic space are given, and a particular investigation of entire graphs constructed over the fiber of the ambient space is also made. Our approach is based on a parabolicity criterion related to a linearized differential operator which is a divergence-type operator and can be regarded as a natural extension of the standard Laplacian.

• Honam Mathematical Journal
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• v.18 no.1
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• pp.79-83
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• 1996

• Honam Mathematical Journal
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• v.4 no.1
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• pp.29-40
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• 1982

• Kyungpook Mathematical Journal
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• v.8 no.1
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• pp.15-22
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• 1968

• Kyungpook Mathematical Journal
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• v.25 no.1
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• pp.15-28
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• 1985

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.603-611
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• 2020

The purpose of this note is to introduce a type of Riemannian manifold called an almost quasi Ricci symmetric manifold and investigate the several properties of such a manifold on which some geometric conditions are imposed. And the existence of such a manifold is ensured by a proper example.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.867-871
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• 2013

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $s^{\prime}^*_g{\neq}0$, which generalizes the previous partial results.

• Publications of The Korean Astronomical Society
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• v.8 no.1
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• pp.199-206
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• 1993

We review recent systematic investigation of the X-ray spectra of early type galaxies by using the Einstein data base and present new results by the ROSAT observations. The Einstein data suggested that the galaxies with low X-ray to optical luminosity ratio may have another very soft component. ROSAT observations confirm its presence and call for further study to understand the nature of this very soft emission. The X-ray bright galaxies have emission temperature of ${\sim}\;0.8\;keV$ and show radial gradients in the sense that X-ray emission is softer and more absorbed in the inner region.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1441-1456
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• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.