A lower bound for eigenvalue of Laplace operator on locally symmetric space

2010 ◽  
Author(s):  
Yufa Huang
Keyword(s):  
Lower Bound ◽  
Symmetric Space ◽  
Laplace Operator ◽  
Locally Symmetric Space

scholarly journals On some compact almost Kähler locally symmetric space

1998 ◽  
Vol 21 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Takashi Oguro
Keyword(s):  
Symmetric Space ◽  
Scalar Curvature ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Symmetric Space ◽  
Kahler Manifold ◽  
Almost Kähler

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric spaceMis a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, thenMis a Kähler manifold.

scholarly journals Hyperbolic rank rigidity for manifolds of -pinched negative curvature

2018 ◽  
Vol 40 (5) ◽  
pp. 1194-1216
Author(s):  
CHRIS CONNELL ◽  
THANG NGUYEN ◽  
RALF SPATZIER
Keyword(s):  
Riemannian Manifold ◽  
Symmetric Space ◽  
Sectional Curvature ◽  
Negative Curvature ◽  
Jacobi Field ◽  
Rigidity Result ◽  
Locally Symmetric Space ◽  
Rank One ◽  
Sectional Curvatures

A Riemannian manifold $M$ has higher hyperbolic rank if every geodesic has a perpendicular Jacobi field making sectional curvature $-1$ with the geodesic. If, in addition, the sectional curvatures of $M$ lie in the interval $[-1,-\frac{1}{4}]$ and $M$ is closed, we show that $M$ is a locally symmetric space of rank one. This partially extends work by Constantine using completely different methods. It is also a partial counterpart to Hamenstädt’s hyperbolic rank rigidity result for sectional curvatures $\leq -1$, and complements well-known results on Euclidean and spherical rank rigidity.

scholarly journals Principal frequency of the p-Laplacian and the inradius of Euclidean domains

2015 ◽  
Vol 07 (03) ◽  
pp. 505-511 ◽  
Author(s):  
Guillaume Poliquin
Keyword(s):  
Lower Bound ◽  
Laplace Operator ◽  
Lower Bounds ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Planar Domains ◽  
Principal Frequency ◽  
The Laplace Operator ◽  
Simply Connected ◽  
Euclidean Domains

We study the lower bounds for the principal frequency of the p-Laplacian on N-dimensional Euclidean domains. For p > N, we obtain a lower bound for the first eigenvalue of the p-Laplacian in terms of its inradius, without any assumptions on the topology of the domain. Moreover, we show that a similar lower bound can be obtained if p > N - 1 assuming the boundary is connected. This result can be viewed as a generalization of the classical bounds for the first eigenvalue of the Laplace operator on simply connected planar domains.

scholarly journals An example of rank two symmetric Osserman space

1997 ◽  
Vol 56 (3) ◽  
pp. 517-521 ◽  
Author(s):  
Zoran Rakić
Keyword(s):  
Symmetric Space ◽  
Riemannian Manifolds ◽  
Explicit Construction ◽  
Quaternionic Structure ◽  
Locally Symmetric Space ◽  
Rank 2

Recently, Blažić, Bokan and Rakić, obtained some classes of 4-dimensional Osserman pseudo-Riemannian manifolds. One of these is the class of rank 2 locally symmetric space endowed with an integrable para-quaternionic structure. In this paper we give an explicit construction of an example of a space of that kind.

Geometry of the SU (2) Di-Meron Solution

1986 ◽  
Vol 41 (4) ◽  
pp. 571-584
Author(s):  
R. Brucker ◽  
M. Sorg
Keyword(s):  
Symmetric Space ◽  
Geometric Structure ◽  
Analytic Form ◽  
Riemannian Structure ◽  
Conformally Flat ◽  
Geometric Properties ◽  
Yang Mills ◽  
Locally Symmetric Space ◽  
Meron Solution

The geometric properties of the di-m eron solution to the SU (2) Yang-Mills equations are studied in detail. The essential geometric structure of this solution is that of a locally symmetric space endowed with a Riemannian structure which is conformally flat. The di-meron solution is representable by an integrable 3-distribution over Euclidean 4-space. The corresponding integral surfaces are obtained in analytic form.

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