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Various Ricci Identities in Finsler Space

Published online by Cambridge University Press:  09 April 2009

H. D. Pande
H. D. Pande
Affiliation:
Department of Mathematics University of Gorakhpur Gorakhpur India and Department of Mathematics University of Western Australia Nedlands, W.A.
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Ricci identities in a Finsler space have been given by C. I. Ispas [1], H. Rund [2], R. S. Mishra and H. D. Pande [3] and others. Here we shall prove some identities using the principle of mathematical induction. Considering a second order contravariant tensor depending on the element of support , we have the following theorems.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 228 - 232
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Ispas, C.I., ‘Identite' de type Ricci dans l'’, Com. Acad. R.P.Române 2 (1952), 13–18.Google Scholar
[2]Rund, H., The Differential Geometry of Finsler spaces (Springer Verlag, Berlin, 1959).CrossRefGoogle Scholar
[3]Mishra, R. S. and Pande, H. D., ‘The Ricci Identity, Annali di Matematica, pura ed applicata 75 (1967), 355–361.CrossRefGoogle Scholar
[4]Mishara, R. S., A course in tensor with application to Riemannian Geometry (Pothishala Pvt. Ltd. Alld., India, 1965).Google Scholar
[5]Misra, R. B., Some problems in Finsler space (ph.D.Thesis, University of Allahabad, 1967).Google Scholar