1,720,966 research outputs found
A characterization of H-strictly convex hypersurfaces in hyperbolic space by the Ricci curvatures
No full textInternational Conference on Differencial Geometry and Dynamical Systems (DGDS) -- OCT 08-11, 2009 -- Bucharest, ROMANIAIn previous papers the first author obtained some upper bound estimations for the Ricci curvatures of the hypersurfaces in a sphere ([6]) and in a hyperbolic manifold ([4], [5]) by the extremum principle. In the present paper, we introduce an H-strictly convex hypersurface in the hyperbolic space N(n+1) and using a result given by B.Y.Chen in [2] we give a lower bound approximation for the Ricci curvature of a H-strictly convex hypersurface in N(n+1).Romanian Acad, Inst Mah, Inst Solid Mech,Acad Romanian Sci,Univ Bucharest, Fac Mah,Univ Politehnica Bucharest, Fac Appl Sci,Tech Univ Civil Engn Bucharest,Balkan Soc Geometers,Romanian Fulbright Alumni Assoc,Romanian Simulat So
A characterization of H-strictly convex hypersurfaces in hyperbolic space by the Ricci curvatures
No full textInternational Conference on Differencial Geometry and Dynamical Systems (DGDS) -- OCT 08-11, 2009 -- Bucharest, ROMANIAIn previous papers the first author obtained some upper bound estimations for the Ricci curvatures of the hypersurfaces in a sphere ([6]) and in a hyperbolic manifold ([4], [5]) by the extremum principle. In the present paper, we introduce an H-strictly convex hypersurface in the hyperbolic space N(n+1) and using a result given by B.Y.Chen in [2] we give a lower bound approximation for the Ricci curvature of a H-strictly convex hypersurface in N(n+1).Romanian Acad, Inst Mah, Inst Solid Mech,Acad Romanian Sci,Univ Bucharest, Fac Mah,Univ Politehnica Bucharest, Fac Appl Sci,Tech Univ Civil Engn Bucharest,Balkan Soc Geometers,Romanian Fulbright Alumni Assoc,Romanian Simulat So
Generalized Helices On N-Dimensional Riemann-Otsuki Spaces
No full textIn this paper the well-known properties of helices in Euclidian 3-space are extended to n-dimensional Riemann-Otsuki space. We define the infinitesimal deformations of curves in Riemann-Otsuki space and obtain the condition such that the given deformation of a curve defines a generalized Helix in this space
Null Hybrid Curves and Some Characterizations of Null Hybrid Bertrand Curves
Get PDFIn this paper, we investigate null curves in R24, the four-dimensional Minkowski space of index 2, utilizing the concept of hybrid numbers. Hybrid and spatial hybrid-valued functions of a single variable describe a curve in R24. We first derive Frenet formulas for a null curve in R23, the three-dimensional Minkowski space of index 2, by means of spatial hybrid numbers. Next, we apply the Frenet formulas for the associated null spatial hybrid curve corresponding to a null hybrid curve in order to derive the Frenet formulas for this curve in R24. This approach is simpler and more efficient than the classical differential geometry methods and enables us to determine a null curve in R23 corresponding to the null curve in R24. Additionally, we provide an example of a null hybrid curve, demonstrate the construction of its Frenet frame, and calculate the curvatures of the curve. Finally, we introduce null hybrid Bertrand curves, and by using their symmetry properties, we provide some characterizations of these curves
On Third Order Bronze Fibonacci Quaternions
No full textIn this study, we define third order bronze Fibonacci quaternions. We obtain the generating functions, the Binet’s formula and some properties of these quaternions. We give d’Ocagne’s-like and Cassini’s-like identity and we use q-determinants for quaternionic matrices to give the Cassini’s identity for third order bronze Fibonacci quaternions
Complete spacelike hypersurfaces with constant scalar curvature and sectional curvatures ? 1 in De Sitter space S16(1)
No full textHypersurfaces with constant scalar curvature and two different principal curvatures isometrically immersed in an (n+1)-dimensional space form M-,M-+1 (C) of constant curvature c and especially in Sn+1(c) have been extensively investigated within the last four decades. In the present work, we study complete spacelike hypersurfaces with constant scalar curvature and have sectional curvatures K(pi) >= 1 in de Sitter space S-1(6)(1) and find a result on the type number of such a hypersurface
On split-octonionic curves
Get PDFIn this paper, we first define the vector product in Minkowski space , which is identified with the space of spatial split-octonions. Next, we derive the frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet-Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the frame and Frenet-Serret frame. Furthermore, we present the Frenet-Serret frame with split octonions in . Finally, we give illustrative examples with Matlab codes.Istanbul Beykent University Scientific Research Projects Coordination Unit [2023- 24-BAP-01, 2024]This research has been supported by Istanbul Beykent University Scientific Research Projects Coordination Unit. Project Number: 2023- 24-BAP-01, 2024
On xi-Conformally and xi-Pseudo Projectively Flat Lorentzian Sasakian Manifolds with Tanaka-Webster Connection
No full textIn this work, the Tanaka-Webster connection on a Lorentzian Sasakian manifold is defined and the notions xi-quasi conformally and xi-pseudo projectively flat structures on a Lorentzian Sasakian manifold are introduced. After that, it is proved that if any Lorentzian Sasakian manifold with Tanaka-Webster connection is an eta- Einstein manifold, then the Thnaka-Webster connection (del) over cap is xi-conformally flat. Furthermore, we give some structure theorems on Lorentzian Sasakian manifold with respect to the Tanaka-Webster connection
On ?-Conformally and ?-Pseudo Projectively Flat Lorentzian Sasakian Manifolds with Tanaka-Webster Connection
Get PDFIn this work, the Tanaka-Webster connection on a Lorentzian Sasakian manifold is defined and the notions xi-quasi conformally and xi-pseudo projectively flat structures on a Lorentzian Sasakian manifold are introduced. After that, it is proved that if any Lorentzian Sasakian manifold with Tanaka-Webster connection is an eta- Einstein manifold, then the Thnaka-Webster connection (del) over cap is xi-conformally flat. Furthermore, we give some structure theorems on Lorentzian Sasakian manifold with respect to the Tanaka-Webster connection
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