Differential geometry of curves in centro-Euclidean spaces

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

Contributions to differential geometry of spacelike curves in Lorentzian plane L2

‎In this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the‎ ‎special curves mentioned above are studied in Lorentzian plane $mathbb{L}%‎‎^{2}.$ Finally some characterizations of these special curves are given in‎ ‎$mathbb{L}^{2}.$‎

DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 2. Curves in Space

for a < t < b. The entire Section 1.3 of the notes can be immediately reformulated for curves in the space: Definition 1.3.2 (of the length of a curve over a closed interval), Definition 1.3.3 and Theorem 1.3.4 (concerning reparametrization of curves), Definition 1.3.4 (of a regular curve), Theorem 1.3.6 and Proposition 1.3.7 (concerning parametrization by arc length). As about Section 1.4 (tha...

Poisson Geometry of Differential Invariants of Curves in Some Nonsemisimple Homogenous Spaces

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form M ∼= (G n IRn)/G where G ⊂ GL(n, IR) is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold M so th...