Conformal H-vector-change in Finsler Spaces
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Authors
A. Taleshian
- Department of Mathematics, University of Mazandaran, Babolsar, Iran.
D. M. Saghali
- Department of Mathematics, University of Mazandaran, Babolsar, Iran.
S. A. Arabi
- Department of Mathematics, University of Mazandaran, Babolsar, Iran.
Abstract
We investigate what we call a conformal \(h\)-vector-change in Finsler spaces, namely
\[F(x,y)\rightarrow\bar{F}(x,y)=e^{\sigma(x)}F(x,y)+\beta ,\]
where, \(\sigma\) is a function of \(x\) only, and \(\beta(x,y):=b_i(x,y)y^i\), where \(b_i:=b_i(x,y)\) is an \(h\)-vector. This change generalizes various types of changes: conformal changes, generalized Randers changes, Randers change. Under this change, we obtain the relationships between some tensors associated with \((M,F)\) and the corresponding tensors associated with \((M,\bar{F})\). Next, we express the conditions for more generalized \(m\)-th root metrics \(\tilde{F}_1=\sqrt{A_1^{\frac{2}{m_1}}+B_1+C_1}\) and \(\tilde{F}_2=\sqrt{A_2^{\frac{2}{m_2}}+B_2+C_2}\), when is established conformal \(h\)-vector-change and \(m_1, m_2\) are even numbers and other case \(m_1, m_2\) even and odd numbers, respectively. Finally, we prove that under these conditions conformal \(h\)-vector-change in Finsler spaces reduces to conformal \(\beta\)-change in Finsler spaces.
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ISRP Style
A. Taleshian, D. M. Saghali, S. A. Arabi, Conformal H-vector-change in Finsler Spaces, Journal of Mathematics and Computer Science, 7 (2013), no. 4, 249 - 257
AMA Style
Taleshian A., Saghali D. M., Arabi S. A., Conformal H-vector-change in Finsler Spaces. J Math Comput SCI-JM. (2013); 7(4):249 - 257
Chicago/Turabian Style
Taleshian, A., Saghali, D. M., Arabi, S. A.. "Conformal H-vector-change in Finsler Spaces." Journal of Mathematics and Computer Science, 7, no. 4 (2013): 249 - 257
Keywords
- \(m\)-th root metric
- more generalized \(m\)-th root metric
- generalized Randers change.
MSC
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