نتایج جستجو برای: ricci operator

تعداد نتایج: 98899  

2008
Shu-Yu Hsu

In this paper we will give a rigorous proof of the lower bound for the scalar curvature of the standard solution of the Ricci flow conjectured by G. Perelman. We will prove that the scalar curvature R of the standard solution satisfies R(x, t) ≥ C0/(1−t) ∀x ∈ R , 0 ≤ t < 1, for some constant C0 > 0. Recently there is a lot of study of Ricci flow on manifolds by R. Hamilton [H1-6], S.Y. Hsu [Hs1...

Journal: :Journal of Functional Analysis 2021

We compute the spectra of Laplace-Beltrami operator, connection Laplacian on 1-forms and Einstein operator symmetric 2-tensors sine-cone over a positive manifold $(M, g)$. conclude under which conditions $(M,g)$, is dynamically stable singular Ricci-de Turck flow rigid as

2008
JUN LING

The study of behavior of the eigenvalues of differential operators along the flow of metrics is very active. We list a few such studies as follows. Perelman [9] proved the monotonicity of the first eigenvalue of the operator −∆ + 1 4 R along the Ricci flow by using his entropy and was then able to rule out nontrivial steady or expanding breathers on compact manifolds. X. Cao [1] and J. F. Li [6...

Journal: :bulletin of the iranian mathematical society 0
s. k. hui department of mathematics, sidho kanho birsha university, purulia-723104, west bengal, india.newline department of mathematics, bankura university, bankura-722155, west bengal, india. y. matsuyama department of mathematics, chuo university, faculty of science and engineering, 1-13-27 kasuga, bunkyo-ku, tokyo 112-8551, japan.

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

2004
Y. Nikolayevsky

A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...

Journal: :iranian journal of science and technology (sciences) 2006
m. bektas

let (m,g ) be a compact immersed hypersurface of (rn+1,) , λ1 the first nonzeroeigenvalue, α the mean curvature, ρ the support function, a the shape operator, vol (m ) the volume of m,and s the scalar curvature of m. in this paper, we established some eigenvalue inequalities and proved theabove.1) 1 2 2 2 2m ma dv dvn∫ ρ ≥ ∫ α ρ ,2)( )2 2 1 2m 1 mdv s dvn nα ρ ≥ ρ∫ − ∫ ,3) if the scalar curvatu...

2003
Lei Ni LEI NI

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to four such that the Ricci flow does not preserve the nonnegativity of the sectio...

2009
R. K. RAINA AHMET YILDIZ

The object of the present paper is to study three-dimensional Lorentzian -Sasakian manifolds which are Ricci-semisymmetry, locally symmetric and have -parallel Ricci tensor. An example of a three-dimensional Lorentzian -Sasakian manifold is given which verifies all the Theorems.

2008
Stefan Ivanov

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

2009
Jun Ling Zhiqin Lu

In this paper, we first give a short review of the eigenvalue estimates of Laplace operator and Schrödinger operators. Then we discuss the evolution of eigenvalues along the Ricci flow, and two new bounds of the first eigenvalue using gradient estimates. 2000 Mathematics Subject Classification: 58J50, 35P15, 53C21.

نمودار تعداد نتایج جستجو در هر سال

با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید