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Cubo (Temuco)

versão On-line ISSN 0719-0646

Cubo vol.14 no.1 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000100007 

CUBO A Mathematical Journal Vol.14, N° 01, (81-91). March 2012

 

Special Recurrent Transformation in an NPR-Finsler Space

Anjali Goswami

Department of Mathematics Jagannath Gupta Institute of Engineering and Technology Sitapura, Jaipur, India email: dranjaligoswami@rediffmail.com


ABSTRACT

In this paper, an infinitesimal transformation , where the vector vi is recurrent has been considered in an NPR- Finsler space. Such transformation is being called special recurrent transformation if the recurrence vector of the NPR- Finsler space is Lie invariant. Besides different properties of such transformation, the conditions for such transformation to be curvature collineation and an afine motion have been obtained.

Keywords and Phrases: NPR-Finsler space, recurrent vector fields, special recurrent transformation, curvature collineation, affne motion.


RESUMEN

En este artículo se considera una transformación infinitesimal , donde el vector vi es recurrente, en un espacio NPR- Finsler. Tal transformación se dice transformación recurrente especial si el vector recurrente del espacio NPR- Finsler es Lie invariante. Además se han obtenido diferentes propiedades de dicha transformación y las condiciones para que ésta sea una colineación de curvatura y una moción afín.

2010 AMS Mathematics Subject Classification: 53B40.


 

References

[1] Pandey, P. N., A recurrent Finsler manifold admitting special transformations, Progress of Mathematics, 13 (1979), 85-98.         [ Links ]

[2] Pandey, P. N., On NPR-Finsler manifold, Ann. Fac. Kinshasha, 6 (1980), 65-77.         [ Links ]

[3] Pandey, P. N., Affne motion in a recurrent Finsler manifold, Ann. Fac. Kinshasha, 6 (1980), 51-63.         [ Links ]

[4] Pandey, P. N., Some identities in an NPR-Finsler manifold, Proc. Nat. Acad. Sci. (India), 51 (1981), 105-109.         [ Links ]

[5] Pandey, P. N., Certain types of affne motion in a Finsler manifold, Colloquium Mathematicum, 49 (1985), 243-252.         [ Links ]

[6] Rund, H., The Differential Geometry of Finsler spaces, Springer-Verlag, Berlin, 1959.         [ Links ]

[7] Yano, K., The theory of Lie derivatives and its applications, North Holland Publ. Co., Amsterdam, 1957.         [ Links ]


Received: September 2010. Revised: May 2011.