Hypersurfaces of a projective Kropina conformal change
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 Fn1 remains to be a totally
geodesic hypersurface Fn1 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); PP6371
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
Issue
Section
License
Copyright Notice
Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication.
Copyrights for articles published in World Scholars journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.