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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Manno Gianni, Vollmer Andreas
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2018
Materias:	projective connections benenti tensors projectively equivalent metrics levi-civita metrics 53a20 53b10 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/69574509794c40c8b0828478926b1cc7
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:69574509794c40c8b0828478926b1cc7
record_format	dspace
spelling	oai:doaj.org-article:69574509794c40c8b0828478926b1cc72021-12-02T19:07:54ZBenenti Tensors: A useful tool in Projective Differential Geometry2300-744310.1515/coma-2018-0006https://doaj.org/article/69574509794c40c8b0828478926b1cc72018-05-01T00:00:00Zhttps://doi.org/10.1515/coma-2018-0006https://doaj.org/toc/2300-7443Two 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.Manno GianniVollmer AndreasDe Gruyterarticleprojective connectionsbenenti tensorsprojectively equivalent metricslevi-civita metrics53a2053b10MathematicsQA1-939ENComplex Manifolds, Vol 5, Iss 1, Pp 111-121 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	projective connections benenti tensors projectively equivalent metrics levi-civita metrics 53a20 53b10 Mathematics QA1-939
spellingShingle	projective connections benenti tensors projectively equivalent metrics levi-civita metrics 53a20 53b10 Mathematics QA1-939 Manno Gianni Vollmer Andreas Benenti Tensors: A useful tool in Projective Differential Geometry
description	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.
format	article
author	Manno Gianni Vollmer Andreas
author_facet	Manno Gianni Vollmer Andreas
author_sort	Manno Gianni
title	Benenti Tensors: A useful tool in Projective Differential Geometry
title_short	Benenti Tensors: A useful tool in Projective Differential Geometry
title_full	Benenti Tensors: A useful tool in Projective Differential Geometry
title_fullStr	Benenti Tensors: A useful tool in Projective Differential Geometry
title_full_unstemmed	Benenti Tensors: A useful tool in Projective Differential Geometry
title_sort	benenti tensors: a useful tool in projective differential geometry
publisher	De Gruyter
publishDate	2018
url	https://doaj.org/article/69574509794c40c8b0828478926b1cc7
work_keys_str_mv	AT mannogianni benentitensorsausefultoolinprojectivedifferentialgeometry AT vollmerandreas benentitensorsausefultoolinprojectivedifferentialgeometry
_version_	1718377154257879040

Benenti Tensors: A useful tool in Projective Differential Geometry

Ejemplares similares