A boundary value problem in the hyperbolic space.
A bridge principle for minimal and constant mean curvature submanifolds of RN.
A characterization for isometries and conformal mappings of pseudo-Riemannian manifolds.
A characterization of a minimal submanifold in
A characterization of Chen surfaces in .
A characterization of collineations by order geometry.
A characterization of hyperspheres in the quaternionic space
A characterization of n-dimensional hypersurfaces in with commuting curvature operators
Let Mⁿ be a hypersurface in . We prove that two classical Jacobi curvature operators and commute on Mⁿ, n > 2, for all orthonormal pairs (x,y) and for all points p ∈ M if and only if Mⁿ is a space of constant sectional curvature. Also we consider all hypersurfaces with n ≥ 4 satisfying the commutation relation , where , for all orthonormal tangent vectors x,y,z,w and for all points p ∈ M.
A characterization of osculating maps
A characterization of regular saddle surfaces in the hyperbolic and spherical three-space.
A class of boundary problems for extremal surfaces of mixed type in Minkowski 3-space.
A class of projectively flat surfaces.
A classfication of 3-type curves in Minkowski 3-space . II.
A classification of 3-type curves in Minkowski 3-space . I.
A classification of 3-type curves in Minkowski 3-space e_1^3, II
A common characterization of the curvature axis for ruled surfaces and curves. (Eine gemeinsame Kennzeichnung der Krümmungsachse bei Regelflächen und Kurven.)
A conjecture on minimal surfaces
Simple computations support the conjecture that a small spherical surface with its center on a minimal surface cannot be divided by the minimal surface into two portions with different area.
A contribution to the Cartan's method of specialization of frames
A contribution to the connection of V. Hlavatý
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...