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On the Projective Algebra of Randers Metrics of Constant Flag Curvature
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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On the Projective Algebra of Randers Metrics of Constant Flag Curvature
Інший ID:
2010 Mathematics Subject Classification: 53C60; 53B50, 58J60
DOI: http://dx.doi.org/10.3842/SIGMA.2011.085
DOI: http://dx.doi.org/10.3842/SIGMA.2011.085
Посилання:
On the Projective Algebra of Randers Metrics of Constant Flag Curvature / M. Rafie-Rad, B. Rezaei // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ.
Підтримка:
The authors would like to express their grateful thanks to the referees for their valuable comments. This work was supported in part by the Institute for Research in Fundamental Sciences (IPM) by the grant No. 89530036. The first author wishes to thank Borzoo Nazari for many fruitful conversations.
Дата:
2011
Переглядів:
579
Завантажень:
279
Анотація:
The collection of all projective vector fields on a Finsler space (M,F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra denoted by p(M,F) and is the Lie algebra of the projective group P(M,F). The projective algebra p(M,F=α+β) of a Randers space is characterized as a certain Lie subalgebra of the projective algebra p(M,α). Certain subgroups of the projective group P(M,F) and their invariants are studied. The projective algebra of Randers metrics of constant flag curvature is studied and it is proved that the dimension of the projective algebra of Randers metrics constant flag curvature on a compact n-manifold either equals n(n+2) or at most is n(n+1)/2.
