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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Some properties of biconcircular gradient vector fields; pp. 162–169

(Full article in PDF format) doi: 10.3176/proc.2009.3.03


Authors

Adela Mihai

Abstract

We consider a Riemannian manifold carrying a biconcircular gradient vector field X, having as generative a closed torse forming U. The existence of such an X is determined by an exterior differential system in involution depending on two arbitrary functions of one argument. The Riemannian manifold is foliated by Einstein surfaces tangent to X and U. Properties of the biconcircular vector field X  are investigated.

Keywords

differential geometry, biconcircular gradient vector field, skew-symmetric Killing vector field, closed torse forming.

References

1. Cartan , E. Systèmes Différentiels Extérieurs et Leurs Applications Géométriques. Hermann , Paris , 1975.

2. Dieudonné , J. Elements d’Analyse , Vol. IV. Gauthier Villars , Paris , 1977.

3. Matsumoto , K. , Mihai , A. , and Rosca , R. Riemannian manifolds carrying a pair of skew symmetric Killing vector field. An. Şt. Univ. “Al. I. Cuza” Iaşi , 2003 , 49 , 137–146.

4. Mihai , I. , Rosca , R. , and Verstraelen , L. Some Aspects of the Differential Geometry of Vector Fields. K.U. Leuven , K.U. Brussel , PADGE 2 , 1996.

5. O’Neill , B. Semi-Riemannian Geometry. Academic Press , 1983.

6. Poor , W. A. Differential Geometric Structures. McGraw Hill , New York , 1981.

7. Reyes , E. and Rosca , R. On biconcircular gradient vector fields. Rend. Sem. Mat. Messina Serie II , 1999 , 6 (21) , 13–25.

8. Rosca , R. An exterior concurrent skew-symmetric Killing vector field. Rend. Sem. Mat. Messina , 1993 , 2 , 131–145.

9. Yano , K. On torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo , 1984 , 20 , 340–345.
doi:10.3792/pia/1195572958

 
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Current Issue: Vol. 68, Issue 3, 2019




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No. 1: 20 March
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