Hypersurfaces of a projective Kropina conformal change

Authors

  • T. N. Pandey Kumar Vineet Suraj Kumar Shukla Department of mathematics and statistics D. D. U. Gorakhpur University, Gorakhpur

Keywords:

Total solid, Total suspended solid, pH, Biochemical oxygen demand and turbidity.

Abstract

In the year 1984 Shibata investigated the theory of a change
which is called a -change of a Finsler metric. On the other hand in
1985 a systematic study of geometry of hypersurfaces in Finsler spaces
was given by Matsumoto. The present paper is devoted to study the
condition for a Kropina conformal change to be projective and nd out
when a totally geodesic hypersurfaces Fn􀀀1 remains to be a totally
geodesic hypersurface Fn􀀀1 under the projective Kropina conformal
change. Further we obtained the condition under which a Finslarian
hypersurfaces given by the projective Kropina cinformal change are
projectively at

References

Basco S. and Matsumoto M.:- Projective change between Finsler

spaces with (; ) metric, Tensor N. S., 55(1994); 232 􀀀 257.

Chaubey V. K. and Kumar Pradeep:- Hypersurfaces of a projective

rander conformal change, J. Nat. Acad. Math, V ol:27(2013); PP63􀀀71

Hashiguchi M.:- On conformal transformation of Finsler metric, J.

Math. Kyoto university, 16(1976); 25 􀀀 50.

Izumi H.:- Conformal transformation of Finsler space I,Tensor N.S.,

; 33 􀀀 41

Izumi H.:- Conformal transformation of Finsler space II, Tensor N.S.,

; 337 􀀀 359.

Kitayama M.:- Finslerian hypersurface and metric transformation,

Tensor N.S., 60(1998); 171 􀀀 178

Kitayama M.:- On Finslerian hypersurface given by -change, Balkan

journal of geometry and its applications, 722(2002); 49 􀀀 55.

Knebelman M. S.:- Conformal geometry of generalized metric spaces,

Proc. Nat. Acad. Sci. USA, 15(1929)33 􀀀 41and376 􀀀 379

Matsumoto M.:- The induced and intrinsic Finsler connections of a

hypersurface and Finslerian projective geometry,J. Math. Kyoto Uni-

versity, 25(1985); 107 􀀀 144

Pandey T. N. and Tripahi Manish Nath:- Journal of international

academy of physical sciences, V ol:17;No:2; (2013); 113 􀀀 121.

Pradsad B. N. and Tripathi B. K.:- Fimnslerian hypersurface and

Kropina change of a Finsler metric, Journal of tensor society of India,

(2005); 49 􀀀 58:

Rund H.:- The Dierantial Geometry of Finsler Spaces, Springer

Berlin, 1959

Shibata C., Shimada H. and Azuma M.:- On normal curvature of

a hy[per surface of nsler spaces, Anallele Stiintice University "Al. I.

Cuza" Iasi S. I. Mathematica, 31(1985); 97 􀀀 102.

Shukla H. S. and Mishra Arunima:- On Finsler space with rander

conformal change : Main sealers, geodesic and scalar curvature, inter-

national J. Math combine, 3(2012); 20 􀀀 29

Downloads

Published

2016-05-31

Issue

Section

Articles