in this paper, a novel patch geodesic derivative pattern (pgdp) describing the texture map of a face through its shape data is proposed. geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3d images with different pose and expression variations. an extensive experimental investigation is conducted using the publicly available bosphorus and bu-3...

in this paper we study isotropic lagrangian submanifolds , in complex space forms . it is shown that they are either totally geodesic or minimal in the complex projective space , if . when , they are either totally geodesic or minimal in . we also give a classification of semi-parallel lagrangian h-umbilical submanifolds.

A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those...

In this paper, we find the unit tangent vector and the geodesic torsion of the tangential intersection curve of two surfaces in all three types of surface-surface intersection problems (parametric-parametric, implicit-implicit and parametric-implicit) in three-dimensional Euclidean space.

Let X be a geodesic space. We say that X is geodesically complete if every geodesic segment β : [0, a] → X from β(0) to β(a) can be extended to a geodesic ray α : [0,∞) → X, (i.e. β(t) = α(t), for 0 ≤ t ≤ a). If X is a compact npc space (“npc” means: “non-positively curved”) then it is almost geodesically complete, see [10]. (X, with metric d, is almost geodesically complete if its universal co...

In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the literature that are known to have regular curvature invariants.

(d) Domains of dependence and geodesic laminations (§5). This section contains the main theorem in the flat case; essentially that domains of dependence are in one-one correspondence with measured geodesic laminations. First some basic causality; domains of dependence are defined and Proposition 11 describes the structure of the causal horizon. Proposition 12 is one half of the main theorem; gi...

We prove that a hypersurface of a space form with almost constant mean curvature and almost constant scalar curvature is close to a geodesic sphere. In the case of Euclidean space, we deduce new characterizations of geodesic spheres.

We review geometrical properties of a static spacetime (M, g), including geodesic completeness, causality, standard splittings, compact M , closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients β, β −1 (β = −g(K, K), being K a timelike irrotational Killing vector field), which essentially control completeness, ca...

Global geometric properties of product manifolds M = M × R2, endowed with a metric type 〈·, ·〉 = 〈·, ·〉R + 2dudv + H(x, u)du 2 (where 〈·, ·〉R is a Riemannian metric on M and H : M × R → R a function), which generalize classical plane waves, are revisited. Our study covers causality (causal ladder, inexistence of horizons), geodesic completeness, geodesic connectedness and existence of conjugate...