Second eigenvalue of the CR Yamabe operator

2020 ◽  
pp. 2050080
Author(s):  
Flávio Almeida Lemos ◽  
Ezequiel Barbosa
Keyword(s):  
Upper Bound ◽  
Cr Manifold ◽  
Yamabe Invariant ◽  
Pseudo Convex ◽  
Second Eigenvalue

Let [Formula: see text] be a compact, connected, strictly pseudo-convex CR manifold. In this paper, we give some properties of the CR Yamabe Operator [Formula: see text]. We present an upper bound for the Second CR Yamabe Invariant, when the First CR Yamabe Invariant is negative, and the existence of a minimizer for the Second CR Yamabe Invariant, under some conditions.

RESULTS RELATED TO PRESCRIBING PSEUDO-HERMITIAN SCALAR CURVATURE

2013 ◽  
Vol 24 (03) ◽  
pp. 1350020 ◽  
Author(s):  
PAK TUNG HO
Keyword(s):  
Scalar Curvature ◽  
Smooth Function ◽  
The Other ◽  
Cr Manifold ◽  
Geometric Flow ◽  
Yamabe Invariant ◽  
Uniqueness Results ◽  
Other Hand

In this paper, we consider the problem of prescribing pseudo-Hermitian scalar curvature on a compact strictly pseudoconvex CR manifold M. Using geometric flow, we prove that for any negative smooth function f we can prescribe the pseudo-Hermitian scalar curvature to be f, provided that dim M = 3 and the CR Yamabe invariant of M is negative. On the other hand, we establish some uniqueness and non-uniqueness results on prescribing pseudo-Hermitian scalar curvature.

scholarly journals The Bochner-flat cone of a CR manifold

2008 ◽  
Vol 144 (3) ◽  
pp. 747-773
Author(s):  
Liana David
Keyword(s):  
Open Subset ◽  
Kähler Manifold ◽  
Parameter Family ◽  
Local Geometry ◽  
Cr Manifold ◽  
Kähler Structure ◽  
Complex Dimension ◽  
Kahler Manifold ◽  
Pseudo Convex

AbstractWe construct a Kähler structure (which we call a generalised Kähler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a one-parameter family of compatible Sasaki structures. We determine those generalised Kähler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kähler manifold of complex dimension bigger than two is locally isomorphic to a generalised Kähler cone.

scholarly journals The Second Eigenvalue of some Normal Cayley Graphs of Highly Transitive Groups

10.37236/8054 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Xueyi Huang ◽  
Qiongxiang Huang ◽  
Sebastian M. Cioabă
Keyword(s):  
Finite Group ◽  
Upper Bound ◽  
Cayley Graphs ◽  
Recursive Method ◽  
Transitive Groups ◽  
A Finite Group ◽  
Set Of Points ◽  
Second Eigenvalue ◽  
Second Largest Eigenvalue ◽  
Normal Cayley Graphs

Let $G$ be a finite group acting transitively on $[n]=\{1,2,\ldots,n\}$, and  let $\Gamma=\mathrm{Cay}(G,T)$ be a Cayley graph of $G$. The graph $\Gamma$ is called  normal if $T$ is closed under conjugation. In this paper, we obtain an upper bound for the second (largest) eigenvalue of the adjacency matrix of the graph $\Gamma$ in terms of the second eigenvalues of certain subgraphs of $\Gamma$. Using this result, we develop a recursive method to  determine the second eigenvalues of certain  Cayley graphs of $S_n$, and we determine the second eigenvalues  of a majority of the connected normal Cayley graphs (and some of their subgraphs) of $S_n$  with  $\max_{\tau\in T}|\mathrm{supp}(\tau)|\leqslant 5$, where $\mathrm{supp}(\tau)$ is the set of points in $[n]$ non-fixed by $\tau$.

A Note on the Analogue of the Bogomolov Type Theorem on Deformations of CR-Structures

1994 ◽  
Vol 37 (1) ◽  
pp. 8-12 ◽  
Author(s):  
Takao Akahori ◽  
Kimio Miyajima
Keyword(s):  
Line Bundle ◽  
Type Theorem ◽  
Strict Sense ◽  
Weak Version ◽  
Cr Manifold ◽  
Canonical Line Bundle ◽  
Pseudo Convex ◽  
Cr Structures

AbstractLet (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.

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