Invariant Dirac Operators, Harmonic Spinors, and Vanishing Theorems in CR Geometry

被引：0

作者：

Leitner, Felipe ^{[1
]}

机构：

[1] Ernst Moritz Arndt Univ Greifswald, Inst Math & Informat, Walter Rathenau Str 47, D-17489 Greifswald, Germany

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2021年 / 17卷

关键词：

CR geometry; spin geometry; Kohn-Dirac operator; harmonic spinors; Kohn-Rossi cohomology; vanishing theorems;

D O I：

10.3842/SIGMA.2021.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Kohn-Dirac operators D-theta on strictly pseudoconvex CR manifolds with spin(C) structure of weight l is an element of Z. Certain components of D-theta are CR invariants. We also derive CR invariant twistor operators of weight l. Harmonic spinors correspond to cohomology classes of some twisted Kohn-Rossi complex. Applying a Schrodinger-Lichnerowicz-type formula, we prove vanishing theorems for harmonic spinors and (twisted) Kohn-Rossi groups. We also derive obstructions to positive Webster curvature.

引用

页数：25

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