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Scalar curvature comparisons of level hypersurfaces of geodesic spheres

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초록

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

Abstract

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

참고문헌 (10)

  1. R. Bishop, "A relation between volume, mean curvature and diameter", Notices Amer. Math. Soc., 10, pp.364~ (1963)
  2. R. L. Bishop, "Geometry of Manifolds, Pure and Applied Mathematics, Vol. XV" (1964), Academic Press
  3. J. Cheeger, "On the structure of spaces with Ricci curvature bounded below. I", J. Differential Geom., 46(3), pp.406~480 (1997)[DOI]
  4. P. E. Ehrlich, "Volume comparison theorems for Lorentzian manifolds", Geom. Dedicata, 73(1), pp.39~56 (1998)[DOI]
  5. P. E. Ehrlich, "Some semi-Riemannian volume comparison theorems", Tohoku Math. J., 52(3), pp.331~348 (2000)[DOI]
  6. J.-H. Eschenburg, "Comparison theory for Riccati equations", Manuscripta Math., 68(2), pp.209~214 (1990)[DOI]
  7. J.-H. Eschenburg, "Jacobi tensors and Ricci curvature", Math. Ann., 252(1), pp.1~26 (1980)[DOI]
  8. J. R. Kim, "Comparisons of the Lorentzian volumes between level hypersurfaces", J. Geom. Phys., 59(7), pp.1073~1078 (2009)[DOI]
  9. J. R. Kim, "Relative Lorentzian volume comparison with integral Ricci and scalar curvature bound", J. Geom. Phys., 61(6), pp.1061~1069 (2011)[DOI]
  10. D. N. Kupeli, "On conjugate and focal points in semi-Riemannian geometry", Math. Z., 198(4), pp.569~589 (1988)[DOI]

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