query: Let $M$ be a surface. Prove that if the asymptotic curves of $M$ are orthogonal then $M$ is minimal.
positive_passages.docid: 20117
positive_passages.text: Mean curvature in asymptotic directions
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 6960
negative_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
negative_passages.docid: 94434
negative_passages.text: Minimum area of the parallelepiped surface
negative_passages.docid: 155291
negative_passages.text: Prove that for any piecewise smooth curve it is possible to find the parametrisation
negative_passages.docid: 66494
negative_passages.text: Curvature of a curve on a sphere
negative_passages.docid: 96567
negative_passages.text: Immersion of $\mathbb{R}$ to $\mathbb{R}^2$
negative_passages.docid: 128835
negative_passages.text: Compactness of the set of $n \times n$ orthogonal matrices
negative_passages.docid: 66500
negative_passages.text: Proving that orthogonal vectors are linearly independent
negative_passages.docid: 23414
negative_passages.text: Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
negative_passages.docid: 45575
negative_passages.text: why each left ideal of this is minimal?
negative_passages.docid: 27746
negative_passages.text: Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
negative_passages.docid: 156302
negative_passages.text: Find conditions for a surface of rotation to be regular
negative_passages.docid: 63465
negative_passages.text: Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure
negative_passages.docid: 95928
negative_passages.text: Independence and orthogonality
negative_passages.docid: 111348
negative_passages.text: Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$