ON THE EXISTENCE OF BI-INVARIANT FINSLER METRICS ON LIE GROUPS

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LATIFI DARIUSH; TOOMANIAN MEGERDICH

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Journal: MATHEMATICAL SCIENCES Year:2013 | Volume:7 | Issue:- Page(s): 1-5

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Title

ON THE EXISTENCE OF BI-INVARIANT FINSLER METRICS ON LIE GROUPS

Author(s)

LATIFI DARIUSH | TOOMANIAN MEGERDICH | Issue Writer Certificate

Keywords

INVARIANT FINSLER METRIC

BI-INVARIANT METRIC

LIE GROUP

FLAG CURVATURE

HOMOGENEOUS GEODESIC

Abstract

In this paper, we study the geometry of LIE GROUPs with bi-INVARIANT FINSLER METRICs. We first show that every compact LIE GROUP admits a bi-INVARIANT FINSLER METRIC. Then, we prove that every compact connected LIE GROUP is a symmetric Finsler space with respect to the bi-invariant absolute homogeneous Finsler metric. Finally, we show that if G is a LIE GROUP endowed with a bi-INVARIANT FINSLER METRIC, then, there exists a bi-invariant Riemanninan metric on G such that its Levi-Civita connection coincides the connection of F.

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APA: Copy

LATIFI, DARIUSH, & TOOMANIAN, MEGERDICH. (2013). ON THE EXISTENCE OF BI-INVARIANT FINSLER METRICS ON LIE GROUPS. MATHEMATICAL SCIENCES, 7(-), 1-5. SID. https://sid.ir/paper/322674/en

Vancouver: Copy

LATIFI DARIUSH, TOOMANIAN MEGERDICH. ON THE EXISTENCE OF BI-INVARIANT FINSLER METRICS ON LIE GROUPS. MATHEMATICAL SCIENCES[Internet]. 2013;7(-):1-5. Available from: https://sid.ir/paper/322674/en

IEEE: Copy

DARIUSH LATIFI, and MEGERDICH TOOMANIAN, “ON THE EXISTENCE OF BI-INVARIANT FINSLER METRICS ON LIE GROUPS,” MATHEMATICAL SCIENCES, vol. 7, no. -, pp. 1–5, 2013, [Online]. Available: https://sid.ir/paper/322674/en

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