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Öğe A characterization of H-strictly convex hypersurfaces in hyperbolic space by the Ricci curvatures(Geometry Balkan Press, 2010) Erdogan, Mehmet; Alo, JetaIn 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).Öğe A characterization of H-strictly convex hypersurfaces in hyperbolic space by the Ricci curvatures(Geometry Balkan Press, 2010) Erdogan, Mehmet; Alo, JetaIn 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).Öğe Complete spacelike hypersurfaces with constant scalar curvature and sectional curvatures ? 1 in De Sitter space S16(1)(Academic Journals, 2010) Erdogan, Mehmet; Alo, JetaHypersurfaces 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.Öğe The Equations of Motion of a Null Curve in Lightlike Cone of 3-Dimensonal Minkowski Space(Beykent Üniversitesi, 2009) Erdogan, Mehmet; Alo, Jeta; Yilmaz, GulsenIn this article we investigate null curves in the lightlike cone of 3-dimensional Lorentz Minkowski space and give some characterizations of these curves.We also obtain the equations of motion of a null curve in the lightlike cone. Mathematics Subject Classificiation : 53B30, 53B50, 53C80Öğe Generalized Helices On N-Dimensional Riemann-Otsuki Spaces(Beykent Üniversitesi, 2019) Alo, JetaIn 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.Öğe De Moivre-Type Identities for the Padovan Numbers(2021) Akbıyık, Mücahit; Alo, Jeta; Akbıyık, Seda YamaçAt this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers. Also, we define a Padovan sequence with new initial conditions and find some identities between all of these auxiliary sequences. Furthermore, we give quadratic approximations for these sequences.Öğe On ?-Conformally and ?-Pseudo Projectively Flat Lorentzian Sasakian Manifolds with Tanaka-Webster Connection(Chiang Mai Univ, Fac Science, 2022) Erdogan, Mehmet; Alo, JetaIn 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.Öğe On Third Order Bronze Fibonacci Quaternions(Matematikçiler Derneği, 2022) Alo, JetaIn 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.Öğe On Third-Order Bronze Fibonacci Numbers(MDPI, 2021) Akbıyık, Mücahit; Alo, JetaIn this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then, we define the generalized third-order Bronze Fibonacci sequence and calculate the De Moivre-type identities for these sequences. Moreover, we find the generating functions, Binet’s formulas, Cassini’s identities and matrix representations of these sequences and examine some interesting identities related to the third-order Bronze Fibonacci sequences. Finally, we present an encryption and decryption application that uses our obtained results and we present an illustrative example.Öğe SOME PROPERTIES OF LORENTZIAN SASAKIAN MANIFOLDS WITH TANAKA-WEBSTER CONNECTION(Int Center Scientific Research & Studies, 2012) Erdogan, Mehmet; Alo, Jeta; Pirincci, Beran; Yilmaz, GulsenIn this work we study some curvature properties of Lorentzian Sasakian manifolds with respect to the Tanaka-Webster connection and obtain some results about the slant curves of the 3-dimensional Lorentzian Sasakian manifold with Tanaka-Webster connection.
