| Title:
|
Sufficient conditions for convexity in manifolds without focal points (English) |
| Author:
|
Beltagy, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
443-449 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings. (English) |
| Keyword:
|
supporting of subsets |
| Keyword:
|
convex subsets (hypersurfaces) |
| Keyword:
|
conjugate (focal) points |
| Keyword:
|
horospheres |
| MSC:
|
53C20 |
| MSC:
|
53C42 |
| idZBL:
|
Zbl 0797.53034 |
| idMR:
|
MR1243076 |
| . |
| Date available:
|
2009-01-08T18:05:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118601 |
| . |
| Reference:
|
[1] Beltagy M.: Foot points and convexity in manifolds without conjugate points.Bull. Calcutta Math. Soc. 82 (1990), 338-348. Zbl 0749.53033, MR 1134214 |
| Reference:
|
[2] Bishop R.L., Crittenden R.J.: Geometry of Manifolds.Academic Press, New York, 1964. Zbl 0984.53001, MR 0169148 |
| Reference:
|
[3] Bolton J.: Tight immersion into manifolds without conjugate points.Quart. J. Math. Oxford (2) 23 (1982), 159-267. MR 0657122 |
| Reference:
|
[4] Burago Yu.D., Zalgaller V.A.: Sufficient criteria of convexity.J. Soviet Math. (10) 3 (1978), 395-435. Zbl 0389.52001 |
| Reference:
|
[5] Eschenburg J.H.: Horospheres and the stable part of the geodesic flow.Math. Z. 153 (1977), 237-251. Zbl 0332.53028, MR 0440605 |
| Reference:
|
[6] Goto M.S.: Manifolds without focal points.J. Diff. Geom. 13 (1978), 341-359. Zbl 0424.53021, MR 0551564 |
| Reference:
|
[7] Kelly P.J., Weiss M.L.: Geometry and convexity.John Wiley & Sons, Inc., New York, 1979. Zbl 0409.52001, MR 0534615 |
| Reference:
|
[8] Valentine F.A.: Convex Sets.McGraw-Hill, New York, 1964. Zbl 0333.52001, MR 0170264 |
| . |
