Benenti Tensors: A useful tool in Projective Differential Geometry

Benenti Tensors: A useful tool in Projective Differential Geometry

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...

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Bibliographic Details
Published in:Complex manifolds (Warsaw, Poland) Vol. 5; no. 1; pp. 111 - 121
Main Authors: Manno, Gianni, Vollmer, Andreas
Format: Journal Article
Language:English
Published: De Gruyter 18-05-2018
Subjects:
53A20
53B10
Benenti tensors
Levi-Civita metrics
Projective connections
Projectively equivalent metrics
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Summary: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.
ISSN:2300-7443
2300-7443
DOI:10.1515/coma-2018-0006