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ON REDUCED ALMOST GEODESIC MAPPINGS IN RIEMANNIAN SPACES

ON REDUCED ALMOST GEODESIC MAPPINGS IN RIEMANNIAN SPACES DEMONSTRATIO MATHEMATICAVol xvNo 4tmAdam AdamówON REDUCED ALMOST GEODESIC MAPPINGSIN RIEMANNIAN SPACES1. I n t r o d u c t i o nGeneralizing the celebrated Beltrami theorem, Sinjukov [7]proved the following theorem.T h e o r e mA.I f a Hiemannian space V^ ( n > 2 )admits a n o n - t r i v i a l geodesic mapping onto a l o c a l l y symmet r i c V„, then both V_ and V„ are of constant curvatun'nnre.Hiemannian spaces admitting geodesic mappings have beenstudied by many authors ( [l]|, [ 3 ] , [ 5 ] , [ é ] , [ i o ] ) .As a g e n e r a l i z a t i o n of the concept of a geodesic mapping,i t seems to be i n t e r e s t i n g to i n v e s t i g a t e the so-called a l most geodesic mappings. According to Sinjukov [ 8 ] , the R i e mannian space (V n ,g)said to admit an almost geodesicmapping of type 3rg onto (V n ,g), i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON REDUCED ALMOST GEODESIC MAPPINGS IN RIEMANNIAN SPACES

Demonstratio Mathematica , Volume 15 (4): 10 – Oct 1, 1982

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References (2)

Publisher
de Gruyter
Copyright
© by Adam Adamów
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1982-0406
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol xvNo 4tmAdam AdamówON REDUCED ALMOST GEODESIC MAPPINGSIN RIEMANNIAN SPACES1. I n t r o d u c t i o nGeneralizing the celebrated Beltrami theorem, Sinjukov [7]proved the following theorem.T h e o r e mA.I f a Hiemannian space V^ ( n > 2 )admits a n o n - t r i v i a l geodesic mapping onto a l o c a l l y symmet r i c V„, then both V_ and V„ are of constant curvatun'nnre.Hiemannian spaces admitting geodesic mappings have beenstudied by many authors ( [l]|, [ 3 ] , [ 5 ] , [ é ] , [ i o ] ) .As a g e n e r a l i z a t i o n of the concept of a geodesic mapping,i t seems to be i n t e r e s t i n g to i n v e s t i g a t e the so-called a l most geodesic mappings. According to Sinjukov [ 8 ] , the R i e mannian space (V n ,g)said to admit an almost geodesicmapping of type 3rg onto (V n ,g), i

Journal

Demonstratio Mathematicade Gruyter

Published: Oct 1, 1982

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