Skip to main content
MathOverflow

Return to Question

added 4 characters in body
Source Link
jiangsaiyin
jiangsaiyin
  • 689
  • 3
  • 11

M is a hyperbolic cone over an n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 2} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$$M = R \times {}_{\cosh \left( t \right)}N$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

M is a hyperbolic cone over an n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 2} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

M is a hyperbolic cone over an n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 2} \right)$ ie $M = R \times {}_{\cosh \left( t \right)}N$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

added 9 characters in body
Source Link
jiangsaiyin
jiangsaiyin
  • 689
  • 3
  • 11

M is a hyperbolic cone over aan n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 1} \right)$$Ric(N) \ge - \left( {n - 2} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

M is a hyperbolic cone over a Riemannian manifold N with $Ric(N) \ge - \left( {n - 1} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

M is a hyperbolic cone over an n-1 dim Riemannian manifold N with $Ric(N) \ge - \left( {n - 2} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.

Source Link
jiangsaiyin
jiangsaiyin
  • 689
  • 3
  • 11

Must a hyperbolic cone over Riemannian manifold be manifold?

M is a hyperbolic cone over a Riemannian manifold N with $Ric(N) \ge - \left( {n - 1} \right)$ ie $dS_M^2 = d{t^2} + {\cosh ^2}(t)dS_N^2$,Surely N is an Alexandrov space,must M be a manifold?must N be totally geodesic in M?If not,please give counterexamples and point out the singular points.