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ON A SYMMETRIC TENSOR FIELD IN AREAL SPACE OF SUBMETRIC CLASS

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 2004-2005
Author NameFaculty of Author
Abstract (2. Language): 
The theory of isotropic areal space of submetric class was studied by Kawaguchi and Tandai (1952), Kikuchi (1968) and others . A symmetric curvature tensor field was defined and studied by the present author (1993) in generalized Finsler space. S.M.Uppal and the author (1996) have obtained Veblen identities in special Kawaguchi space . The purpose of the present paper is to define a symmetric tensor field and obtain its Bianchi and Veblen identities . The recurrence property of this tensor is dealt with in the last section of this paper .
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FULL TEXT (PDF): 
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59-68
  • English

REFERENCES

References: 

[1] Kawaguchi A. and Tandai K. (1952) . In areal spaces V. Normalised metric and Connection parameters in an areal space of submetric class . Tensor, N.S ,2 , 47-58 .
[2] Kikuchi S. ( 1968) . Some properties of the curvature tensor in an areal space of Submetric class . Tensor N.S ., 19 , 179-182 .
[3] Singh S.P. (1976). Veblen identity and some tensors in Finsler spaces . Ann. Fac. Sci. de Kinshasa ,Sec. Math-Phy ., 2, 285-294.
[4] S.P.Singh (1993) . On a symmetric curvature tensor field in generalized Finsler Space . Proc. Kenya Math. Soc., 1, 46-49 .
[5] Tandai K. (1953) . On areal spaces VI. On the characterization of metric areal Spaces . Tensor N.S., 3 , 40-45 .
[6] Uppal S.M. and Singh S.P. (1996) . Veblen identities and their equivalence in Special Kawaguchi space . E.U. Journal, 1, 284-291 .
[7] Vranceanu Gh. (1957) . Lecons des g'eome'trie differentials , Bucuresti, 1,200-201 .

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