On pinching theorems for compact pseudo-umbilical submanifold

Global Pinching Theorems of Submanifolds in Spheres

Let M be a compact embedded submanifold with parallel mean curvature vector and positive Ricci curvature in the unit sphere Sn+p (n≥ 2, p ≥ 1). By using the Sobolev inequalities of P. Li (1980) to Lp estimate for the square length σ of the second fundamental form and the norm of a tensor φ, related to the second fundamental form, we set up some rigidity theorems. Denote by ‖σ‖p the Lp norm of σ...

Pinching Theorems for Teardrops and Footballs of Revolution

In this paper, a first step is made in answering a question posed by Thurston in [5) where he asks for the best pinching constant for Riem~an metrics on the so-called teardrop and football orbifolds. Recall that given integers 1 ~ p ~ q, a (p, q)-football F is an orbifold whose underlying space is S2 , and whose singular locus consists of two points. An open neighbourhood of one of these points...

On Properties Characterizing Pseudo- Compact Spaces

Completely regular pseudo-compact spaces have been characterized in several ways. E. Hewitt [6, pp. 68-70] has given one characterization in terms of the Stone-Cech compactification and another in terms of the zero sets of continuous functions. J. Colmez [2; no proofs included] and I. Glicksberg [4] have obtained characterizations by means of a convergence property for sequences of continuous f...

Pseudo Locally Compact Spaces1

Szego Limit Theorems for Toeplitz Operators on Compact Homogeneous Spaces

Let / be a real valued integrable function on a compact homogeneous space M = K\G and M¡ the operator of pointwise multiplication by /. The authors consider families of Toeplitz operators T¡P = PM¡P as P ranges over a net of orthogonal projections from L2(M) to finite dimensional G-invariant subspaces. Necessary and sufficient conditions are given on the net in order that the distribution of ei...