FOCAL SURFACES OF WAVE FRONTS IN THE EUCLIDEAN 3-SPACE
Sign Up to like & getrecommendations! Published in 2018 at "Glasgow Mathematical Journal"
DOI: 10.1017/s0017089518000277
Abstract: Abstract We characterise singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of… read more here.
Keywords: focal surfaces; fronts euclidean; euclidean space; surfaces wave ... See more keywords
Singularities of Slant Focal Surfaces along Lightlike Locus on Mixed Type Surfaces
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14061203
Abstract: There are generally the mixed type surfaces with lightlike locus in the Lorentz-Minkowski 3-space. To investigate the geometry of lightlike locus, we define slant focal surfaces and slant evolutes associated to the oringinal mixed type… read more here.
Keywords: mixed type; focal surfaces; locus; slant focal ... See more keywords
Singularities for Focal Sets of Timelike Sabban Curves in de Sitter 3-Space
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14122471
Abstract: In the theory of cosmology, de Sitter space is the symmetrical model of accelerated expansions of the universe. It is derived from the solution of the Einstein field equation, which has a positive cosmological constant.… read more here.
Keywords: curves sitter; sabban curves; focal surfaces; timelike sabban ... See more keywords