Authors:
P. N. Pandey Department of Mathematics, University of Allahabad, Allahabad, India

Search for other papers by P. N. Pandey in
Current site
Google Scholar
PubMed
Close
and
Shivalika Saxena Department of Mathematics, University of Allahabad, Allahabad, India

Search for other papers by Shivalika Saxena in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The concept of a Lie recurrence was introduced by the first author [6]. It is an infinitesimal transformation with respect to which the Lie derivative of a curvature tensor is proportional to itself. Apart from other results related to a Lie recurrence, it was established that the Weyl projective curvature tensor is Lie recurrent with respect to a Lie recurrence but its converse is not necessarily true. However, an infinitesimal transformation with respect to which the Weyl projective curvature tensor and the Ricci tensor are Lie recurrent, is necessarily a Lie recurrence. Singh [12] studied an infinitesimal transformation with respect to which the Lie derivative of the curvature tensor is proportional to itself and called such transformation as curvature inheritance. Obviously, a curvature inheritance is nothing but a Lie recurrence. Singh [13] also considered a curvature inheritance which is a projective motion and called it a projective curvature inheritance. Gatoto and Singh [1,2] studied -curvature inheritance and projective -curvature inheritance. Pandey and Pandey [9] studied projective Lie recurrence. Mishra and Yadav [3] studied projective curvature inheritance in an NP-Fn. In the present paper we have established that an infinitesimal transformation in a Finsler space is Lie recurrence if and only if the normal projective curvature tensor is Lie recurrent. A part from this result we have generalized almost all theorems of Mishra and Yadav [3].

  • [1] Gatoto, J. K. Singh, S. P. 2008 Projective -curvature inheritance in Finsler spaces Tensor, N. S. 70 17.

  • [2] Gatoto, J. K. Singh, S. P. 2008 -curvature inheritance in Finsler spaces Tensor, N. S. 70 815.

  • [3] Mishra, C. K. Yadav, D. D. S. 2007 Projective curvature inheritance in an NP-Fn Differ. Geom. Dyn. Syst. 9 111121.

  • [4] Pandey, P. N. 1978 CA-collineation in a birecurrent Finsler manifold Tamkang J. Math. 9 7981.

  • [5] Pandey, P. N. 1982 On Lie recurrent Finsler manifolds Indian J. Math. 24 135143.

  • [6] Pandey, P. N. 1982 On a Finsler space of zero projective curvature Acta Math. Acad. Sci. Hungar. 39 387388 .

  • [7] Pandey, P. N. 1987 Non-existence of certain types of NP-Finsler spaces Acta Math. Hungar. 50 7984 .

  • [8] Pandey, P. N. 1980 On NPR-Finsler manifolds Ann. Fac. Sci. Univ. Nat. Zaire (Kinshasa) 6 6577.

  • [9] Pandey, P. N. Pandey, V. 2009 On -curvature inheritance in a Finsler space J. Int. Acad. Phys. Sci. 13 395400.

  • [10] Saxena, S. Pandey, P. N. 2011 On Lie recurrence in a Finsler space Differ. Geom. Dyn. Syst. 13 201207.

  • [11] Rund, H. 1959 The Differential Geometry of Finsler Spaces Springer-Verlag Berlin.

  • [12] Singh, S. P. 2003 On the curvature inheritance in Finsler space Tensor, N. S. 64 211217.

  • [13] Singh, S. P. 2003 Projective curvature inheritance in Finsler space Tensor, N. S. 64 218226.

  • [14] Yano, K. 1957 The Theory of Lie Derivatives and its Applications North-Holland Amsterdam.

  • [15] Misra, R. B. Meher, F. M. 1971 Projective motion in an RNP-Finsler space Tensor, N. S. 22 117120.

  • [16] Misra, R. B. Kishore, N. Pandey, P. N. 1977 Projective motion in an SNP-Fn Boll. Un. Mat. Ital. 14(A) 513519.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2023 14 2 0
Jan 2024 16 0 0
Feb 2024 10 0 0
Mar 2024 13 0 0
Apr 2024 12 0 0
May 2024 10 0 0
Jun 2024 0 0 0