A classification of 3-type curves in Minkowski 3-space . I.
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.
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 ∈...
In this paper the symmetric differential and symmetric Lie derivative are introduced. Using these tools derivations of the algebra of symmetric tensors are classified. We also define a Frölicher-Nijenhuis bracket for vector valued symmetric tensors.
In this paper, under the one-parameter closed planar homothetic motion, a generalization of Holditch Theorem is obtained by using two different line segments (with fixed lengths) whose endpoints move along two different closed curves.