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Öğe BETA BÉZIER CURVES(Institute of Applied Mathematics of Baku State University, 2019) Levent A.; Şahin B.In this paper, we investigate geometric properties of such curves. We construct a new curve by using curves based on new basis with beta functions satisfying various continuity condition and check shape properties. As an interesting property of such curves, we show that the curves based on new basis with beta functions do not have loops which is a useful property for CAGD systems. Since Pythagoren hodograph curves are also important in various CAD applications, we find certain conditions for Pythagorean Hodograph for the curves based on new basis with beta functions. © 2019, Institute of Applied Mathematics of Baku State University. All rights reserved.Öğe Cubic Bezier-like transition curves with new basis functions(Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2018) Levent A.; Şahin B.A cubic trigonometric Bézier-like curve similar to the cubic Bézier curve, with a shape parameter, is presented in this work. With the suitable shape parameter, the cubic trigonometric Bézier-like curves can be made close to the cubic Bézier curves. Then we investigate the condition of smooth connection between non-adjacent cubic trigonometric Bézier-like curves. © 2018, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.Öğe Notes on doubly warped and doubly twisted product CR-submanifolds of kaehler manifolds(2007) Şahin B.Recently, B. Y. Chen studied warped product CR-submanifolds [7] and twisted product CR-submanifolds [6] in Kaehler manifolds. In this paper, we have checked the existence of other product CR-submanifolds such as doubly warped and doubly twisted products in Kaehler manifolds.Öğe On QR-submanifolds of a quaternionic space form(2001) Şahin B.In this paper, we investigate mixed QR-submanifolds in a quaternionic space form and pseudo umbilical QR-submanifold of a quaternionic space form under some additional condition. Finally we give a necessary condition for QR-submanifold of a quaternion Kaehler manifold such that dimv? = 1 to be a 3-quasi Sasakian Manifold. © TÜBİTAK.Öğe Radical anti-invariant lightlike submanifolds of semi-Riemannian product manifolds(2008) Kiliç E.; Şahin B.We introduce radical anti-invariant lightlike submanifolds of a semi Riemannian product manifold and give examples. After we obtain the conditions of integrability of distributions which are involved in the definition of radical anti-invariant lightlike submanifolds, we investigate the geometry of leaves of distributions. We also obtain the induced connection is a metric connection and a radical anti-invariant lightlike submanifold is a product manifold under certain conditions. Finally, we study totally umbilical radical anti-invariant lightlike submanifolds and observe that they are totally geodesic under a condition. © TÜBİTAK.Öğe Semi-invariant submanifolds of Riemannian product manifold(2003) Şahin B.; Atçeken M.In this paper, the geometry of submanifolds of a Riemannian product manifold is studied. Fundamental properties of these submanifolds are investigated such as integrability of distributions, totally umbilical semi-invariant submanifold. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of a Riemannian product manifold to be a locally Riemannian manifold. © Balkan Society of Geometers.Öğe A survey on differential geometry of Riemannian maps between Riemannian manifolds(Sciendo, 2017) Şahin B.The main aim of this paper is to state recent results in Riemannian geometry obtained by the existence of a Riemannian map between Riemannian manifolds and to introduce certain geometric objects along such maps which allow one to use the techniques of submanifolds or Riemannian submersions for Riemannian maps. The paper also contains several open problems related to the research area. © 2017, Sciendo. All rights reserved.
