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Jay
Jay
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Hi there,

Is there any result about the calculation of radius of tubular neighborhood of submanifold inside a Riemannian manifold?

For example, given a simple smooth curve on R^2, what's the radius of its tubular neighborhood? (One upper bound is given by the minimal curvature, but general it is not the radius)

Maybe that is what we can expect: if the curvature of the curve is always decreasing, then the radius of the tubular neighborhood is given by the injective radius of (left) end point, it seems true, right?

For example, they curve is given by: $xy=1, x \in [1,+\infty)$

Thanks!

Hi there,

Is there any result about the calculation of radius of tubular neighborhood of submanifold inside a Riemannian manifold?

For example, given a simple smooth curve on R^2, what's the radius of its tubular neighborhood? (One upper bound is given by the minimal curvature, but general it is not the radius)

Thanks!

Hi there,

Is there any result about the calculation of radius of tubular neighborhood of submanifold inside a Riemannian manifold?

For example, given a simple smooth curve on R^2, what's the radius of its tubular neighborhood? (One upper bound is given by the minimal curvature, but general it is not the radius)

Maybe that is what we can expect: if the curvature of the curve is always decreasing, then the radius of the tubular neighborhood is given by the injective radius of (left) end point, it seems true, right?

For example, they curve is given by: $xy=1, x \in [1,+\infty)$

Thanks!

Source Link
Jay
Jay
  • 583
  • 3
  • 11

radius of tubular neighborhood

Hi there,

Is there any result about the calculation of radius of tubular neighborhood of submanifold inside a Riemannian manifold?

For example, given a simple smooth curve on R^2, what's the radius of its tubular neighborhood? (One upper bound is given by the minimal curvature, but general it is not the radius)

Thanks!