Benenti张量:射影微分几何中的一个有用工具

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-05-18 DOI:10.1515/coma-2018-0006

G. Manno, Andreas Vollmer

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引用次数: 6

摘要

如果两个度量具有相同的测地线(视为未参数化曲线)，则它们被称为射影等效。度量g的可迁移度是度量空间的维数，其射影等价于g。对于同一流形上的任意一对度量(g，)，可以构造一个(1,1)-张量L(g，)，称为Benenti张量。本文讨论了当(g, r)是射影等价时，特别是当迁移度等于2时，Benenti张量的一些几何性质。

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Benenti Tensors: A useful tool in Projective Differential Geometry

Abstract Two metrics are said to be projectively equivalent if they share the same geodesics (viewed as unparametrized curves). The degree of mobility of a metric g is the dimension of the space of the metrics projectively equivalent to g. For any pair of metrics (g, ḡ) on the same manifold one can construct a (1, 1)- tensor L(g, ḡ) called the Benenti tensor. In this paper we discuss some geometrical properties of Benenti tensors when (g, ḡ) are projectively equivalent, particularly in the case of degree of mobility equal to 2.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.