http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES
황승수 호남수학회 2008 호남수학학술지 Vol.30 No.4
On a compact n-dimensional manifold M, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of volume 1, should be Einstein. The purpose of the present paper is to prove that a 3¡dimensional manifold (M,g) is isometric to a standard sphere if ker [수식] and there is a lower Ricci curvature bound. We also study the structure of a compact oriented stable minimal surface in M.
The structure of the regular level sets
황승수 대한수학회 2011 대한수학회보 Vol.48 No.6
Consider the L^2-adjoint [기호] of the linearization of the scalar curvature s_g. If ker [기호]≠0 on an n-dimensional compact manifold, it is well known that the scalar curvature s_g is a non-negative constant. In this paper, we study the structure of the level set φ^(-1)(0) and find the behavior of Ricci tensor when ker[기호]≠0 with s_g>0. Also for a non-trivial solution (g,f) of z=[기호](f) on an n-dimensional compact manifold, we analyze the structure of the regular level set f^(-1). These results give a good understanding of the given manifolds. Consider the L^2-adjoint [기호] of the linearization of the scalar curvature s_g. If ker [기호]≠0 on an n-dimensional compact manifold, it is well known that the scalar curvature s_g is a non-negative constant. In this paper, we study the structure of the level set φ^(-1)(0) and find the behavior of Ricci tensor when ker[기호]≠0 with s_g>0. Also for a non-trivial solution (g,f) of z=[기호](f) on an n-dimensional compact manifold, we analyze the structure of the regular level set f^(-1). These results give a good understanding of the given manifolds.
Three dimensional critical point of the total scalar curvature
황승수 대한수학회 2013 대한수학회보 Vol.50 No.3
It has been conjectured that, on a compact 3-dimensional ori- entable 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′∗ g 6≠ 0, which generalizes the previous partial results.
The critical point equation on a four dimensional warped product manifold
황승수,장정욱 대한수학회 2006 대한수학회보 Vol.43 No.4
On a compact oriented n-dimensional manifold (Mn ;g), it has been conjectured that a metricg satisfying the criticalpoint equation (2) should be Einstein. In this paper, we prove thatif a manifold (M4;g) is a 4-dimensional oriented compact warpedproduct, then g can not be a solution of CPE with a non-zerosolution function f.
Low-energy Prediction of Neutrino Mixing Angles from a Similarity Ansatz
황승수,김시연 한국물리학회 2011 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.59 No.3
We propose to connect a lepton mixing matrix on a high energy scale to a quark mixing matrix by using a similar transformation. This ansatz constrains all the high-energy angles to be under a certain small bound. The similarity between Cabibbo-Kobayashi-Maskawa(CKM) and Potecorvo-Maki-Nakagawa-Sakata(PMNS) significantly narrows the ranges of the physical parameters. The condition requires that sin θ<sub>13</sub> not be larger than 0.15, the masses be of quasi-degenerate normal ordering, and tan be large. Because the predictions from the similarity ansatz are so narrow, they can be tested by experiments in the near future.
Stability of total scalar curvature and the critical point equation
황승수,윤갑진 대한수학회 2024 대한수학회보 Vol.61 No.1
We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.
Critical points and warped product metrics
황승수,장정욱 대한수학회 2004 대한수학회보 Vol.41 No.1
It has been conjectured that, on a compact orientable manifoldM, a critical point of the total scalar curvature functionalrestricted the space of unit volume metrics of constant scalarcurvature is Einstein. In this paper we show that if a manifold isa 3-dimensional warped product, then (M,g) cannot be acritical point unless it is isometric to the standard sphere.
Gradient almost Ricci solitons with vanishing conditions on Weyl tensor and Bach tensor
고진석,황승수 대한수학회 2020 대한수학회지 Vol.57 No.2
In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if {it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers}. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.