Sufficient conditions for convexity in manifolds without focal points

M. Beltagy

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 3, page 443-449
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Beltagy, M.. "Sufficient conditions for convexity in manifolds without focal points." Commentationes Mathematicae Universitatis Carolinae 34.3 (1993): 443-449. <http://eudml.org/doc/247461>.

@article{Beltagy1993,
abstract = {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.},
author = {Beltagy, M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {supporting of subsets; convex subsets (hypersurfaces); conjugate (focal) points; horospheres; supporting sets; no focal points; horodisks},
language = {eng},
number = {3},
pages = {443-449},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sufficient conditions for convexity in manifolds without focal points},
url = {http://eudml.org/doc/247461},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Beltagy, M.
TI - Sufficient conditions for convexity in manifolds without focal points
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 3
SP - 443
EP - 449
AB - 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.
LA - eng
KW - supporting of subsets; convex subsets (hypersurfaces); conjugate (focal) points; horospheres; supporting sets; no focal points; horodisks
UR - http://eudml.org/doc/247461
ER -

References

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  1. Beltagy M., Foot points and convexity in manifolds without conjugate points, Bull. Calcutta Math. Soc. 82 (1990), 338-348. (1990) Zbl0749.53033MR1134214
  2. Bishop R.L., Crittenden R.J., Geometry of Manifolds, Academic Press, New York, 1964. Zbl0984.53001MR0169148
  3. Bolton J., Tight immersion into manifolds without conjugate points, Quart. J. Math. Oxford (2) 23 (1982), 159-267. (1982) MR0657122
  4. Burago Yu.D., Zalgaller V.A., Sufficient criteria of convexity, J. Soviet Math. (10) 3 (1978), 395-435. (1978) Zbl0389.52001
  5. Eschenburg J.H., Horospheres and the stable part of the geodesic flow, Math. Z. 153 (1977), 237-251. (1977) Zbl0332.53028MR0440605
  6. Goto M.S., Manifolds without focal points, J. Diff. Geom. 13 (1978), 341-359. (1978) Zbl0424.53021MR0551564
  7. Kelly P.J., Weiss M.L., Geometry and convexity, John Wiley & Sons, Inc., New York, 1979. Zbl0409.52001MR0534615
  8. Valentine F.A., Convex Sets, McGraw-Hill, New York, 1964. Zbl0333.52001MR0170264

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