Manifolds of almost half of the maximal volume

Author:
Oguz C. Durumeric

Journal:
Proc. Amer. Math. Soc. **104** (1988), 277-283

MSC:
Primary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-1988-0958083-0

Addendum:
Proc. Amer. Math. Soc. **107** (1989), 1145-1146.

MathSciNet review:
958083

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Abstract: The Riemannian manifolds with sectional curvature and volume slightly less (in terms of the dimension and the upper bound of the sectional curvature) than , the half of the volume of the standard sphere, are classified. The behavior of the critical points of the distance function on manifolds whose volume differ from in terms of constructible constants in terms of the dimension is discussed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0958083-0

Keywords:
Curvature,
volume,
diameter

Article copyright:
© Copyright 1988
American Mathematical Society