Classification of complete minimal surfaces in R3 with total curvature 12... .
Classification of five dimensional hypersurfaces with affine normal parallel cubic form.
Classification of homogeneous submanifolds in homogeneous spaces.
Classification of Monge-Ampère equations with two variables
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.
Classification of pencils of conics of type VI in the isotropic plane. (Klassifikationstheorie der Kegelschnittbüschel vom Typ VI der isotropen Ebene.)
Classification of projective space motions with only plane trajectories
The paper contains the solution of the classification problem for all motions in the complex projective space, which have only plane trajectories. It is shown that each such motion is a submanifold of a maximal motion with the same property. Maximal projective space motions with only plane trajectories are determined by special linear submanifolds of dimensions 2, 3, 5, 8 in , they are denoted as and given by explicit expressions.
Classification of surfaces in which are centroaffine-minimal and equiaffine-minimal.
Clifford algebras and possible kinematics.
Clifford algebras, Möbius transformations, Vahlen matrices, and -loops
In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball in -dimensional euclidean space . One notable achievement is a compact, convenient formula for the Möbius loop operation , where the operations on the right are those arising from the Clifford algebra (a formula comparable to for the Möbius loop multiplication...
Clifford fibrations and possible kinematics.
Clifford hypersurfaces in a unit sphere.
Closed space curves of constant curvature consisting of arcs of circular helices.
Closed surfaces with different shapes that are indistinguishable by the SRNF
The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of . Thus, it induces a distance function on the shape space of immersions, i.e., the space...
Codazzi structures induced by minimal affine immersions
We give a necessary and sufficient condition for a Codazzi structure to be realized as a minimal affine hypersurface or a minimal centroaffine immersion of codimension two.
Coincidence set of minimal surfaces for the thin obstacle.
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.
Commensurability classes and volumes of hyperbolic 3-manifolds
Comment on curves in 2- and 3-dimensional Monkowski space.
Commutation formulas for -differentiation in a generalized Finsler space
Commuting linear operators and algebraic decompositions
For commuting linear operators we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential...