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Ali Taghavi
Ali Taghavi
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Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sencesense:

Every geodesic whose tangent vector of its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sence:

Every geodesic whose tangent vector of its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sense:

Every geodesic whose tangent vector of its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

edited body
Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sence:

Every geodesic whose tangent vector ifof its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sence:

Every geodesic whose tangent vector if its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sence:

Every geodesic whose tangent vector of its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.

Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

A non integrable distribution which is totally geodesic

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sence:

Every geodesic whose tangent vector if its intitial point is tangent to the distribution then the tangent vector at all its points is tangent to $D$, too.