Weakly Symmetric Finsler Spaces

2012 ◽  
pp. 135-171
Author(s):  
Shaoqiang Deng
Keyword(s):  
Finsler Spaces ◽  
Weakly Symmetric

scholarly journals On weakly symmetric Finsler spaces

2010 ◽  
Vol 60 (4) ◽  
pp. 570-573 ◽  
Author(s):  
Parastoo Habibi ◽  
Asadollah Razavi
Keyword(s):  
Finsler Spaces ◽  
Weakly Symmetric

WEAKLY SYMMETRIC FINSLER SPACES

2010 ◽  
Vol 12 (02) ◽  
pp. 309-323 ◽  
Author(s):  
SHAOQIANG DENG ◽  
ZIXIN HOU
Keyword(s):  
Open Problem ◽  
Finsler Space ◽  
Finsler Metrics ◽  
Dimensional Sphere ◽  
Finsler Spaces ◽  
Geometrical Properties ◽  
3 Dimensional ◽  
Weakly Symmetric

In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group. This implies that each weakly symmetric Finsler space has vanishing S-curvature. As an application of these results, we prove that there exist reversible non-Berwaldian Finsler metrics on the 3-dimensional sphere with vanishing S-curvature. This solves an open problem raised by Z. Shen.

An Algebraic Approach to Weakly Symmetric Finsler Spaces

2010 ◽  
Vol 62 (1) ◽  
pp. 52-73 ◽  
Author(s):  
Shaoqiang Deng
Keyword(s):  
Large Class ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
Comparison Theorems ◽  
Finsler Spaces ◽  
Volume Comparison ◽  
Algebraic Description ◽  
Interesting Class ◽  
Weakly Symmetric

AbstractIn this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann-Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions 2 and 3. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. Thismeans that reversible non-Berwaldian Finsler spaces with vanishing S-curvaturemay exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces.

On projective symmetries on Finsler spaces

2021 ◽  
Vol 77 ◽  
pp. 101763
Author(s):  
B. Lajmiri ◽  
B. Bidabad ◽  
M. Rafie-Rad ◽  
Y. Aryanejad-Keshavarzi
Keyword(s):  
Finsler Spaces

SOME PROBLEMS IN DECOMPOSED BI-RECURRENT FINSLER SPACES

1984 ◽  
Vol 17 (1) ◽  
Author(s):  
N.K. Sharma ◽  
Asha Srivastava
Keyword(s):  
Finsler Spaces

On warped product Finsler spaces of Landsberg type

2011 ◽  
Vol 52 (9) ◽  
pp. 093506 ◽  
Author(s):  
Ataabak B. Hushmandi ◽  
Morteza M. Rezaii
Keyword(s):  
Warped Product ◽  
Finsler Spaces

New examples of weakly symmetric spaces

1998 ◽  
Vol 125 (4) ◽  
pp. 309-314 ◽  
Author(s):  
J. C. Gonz�lez-D�vila ◽  
L. Vanhecke
Keyword(s):  
Symmetric Spaces ◽  
Weakly Symmetric ◽  
Weakly Symmetric Spaces

ON THE GAUSS–BONNET FORMULA IN RIEMANN–FINSLER GEOMETRY

2002 ◽  
Vol 34 (3) ◽  
pp. 329-340 ◽  
Author(s):  
BRAD LACKEY
Keyword(s):  
Finsler Space ◽  
Finsler Geometry ◽  
Euler Class ◽  
Constant Volume ◽  
Finsler Spaces ◽  
Chern Connection ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Riemannian Case ◽  
Torsion Free

Using Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel–Levi–Civita connection in the Riemannian case), this result extends the Gauss–Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.

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