# Conformal H-vector-change in Finsler Spaces

Volume 7, Issue 4, pp 249 - 257
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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.

### Share and Cite

##### 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.

•  53C60
•  53B40
•  53B05

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