Sufficient conditions for convexity in manifolds without focal points
Beltagy, M.
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 443-449 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1993-01-01
Classification:  53C20,  53C42 
@article{118601,
     author = {M. Beltagy},
     title = {Sufficient conditions for convexity in manifolds without focal points},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {443-449},
     zbl = {0797.53034},
     mrnumber = {1243076},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118601}
}

Beltagy, M. Sufficient conditions for convexity in manifolds without focal points. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 443-449. http://gdmltest.u-ga.fr/item/118601/

Beltagy M. Foot points and convexity in manifolds without conjugate points, Bull. Calcutta Math. Soc. 82 (1990), 338-348. (1990) | MR 1134214 | Zbl 0749.53033

Bishop R.L.; Crittenden R.J. Geometry of Manifolds, Academic Press, New York, 1964. | MR 0169148 | Zbl 0984.53001

Bolton J. Tight immersion into manifolds without conjugate points, Quart. J. Math. Oxford (2) 23 (1982), 159-267. (1982) | MR 0657122

Burago Yu.D.; Zalgaller V.A. Sufficient criteria of convexity, J. Soviet Math. (10) 3 (1978), 395-435. (1978) | Zbl 0389.52001

Eschenburg J.H. Horospheres and the stable part of the geodesic flow, Math. Z. 153 (1977), 237-251. (1977) | MR 0440605 | Zbl 0332.53028

Goto M.S. Manifolds without focal points, J. Diff. Geom. 13 (1978), 341-359. (1978) | MR 0551564 | Zbl 0424.53021

Kelly P.J.; Weiss M.L. Geometry and convexity, John Wiley & Sons, Inc., New York, 1979. | MR 0534615 | Zbl 0409.52001

Valentine F.A. Convex Sets, McGraw-Hill, New York, 1964. | MR 0170264 | Zbl 0333.52001