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Öğe On the integral invariants of kinematically generated ruled surfaces(Shiraz Univ, 2005) Karadag, HB; Keles, SIn this paper, the dual area vector of a closed dual spherical curve is kinematically generated and the dual Steineer vector of a motion are extensively studied by the methods of differential geometry. Jacobi's Theorems, known for real curves, are investigated for closed dual curves. The closed trajectory surfaces generated by an oriented line are fixed in a moving rigid body in IR3, in which the closed dual curves from E. Study's transference principle is studied. The integral invariants of these closed ruled surfaces are calculated by means of the area vector. Moreover, some theorems, results and examples are given.Öğe On the invariant submanifolds of Riemannian product manifold(Springer, 2004) Atceken, M; Keles, SIn this paper, the vertical and horizontal distributions of an invariant sub-manifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant sub-manifold of a Riemannian product manifold to be a locally symmetric and real space form.Öğe Two theorems on invariant submanifolds of product Riemannian manifold(Indian Nat Sci Acad, 2003) Atçeken, M; Keles, SIn this paper we discuss the distributions of a Riemannian almost-product structure in product Riemannian manifold. We show that an invariant submanifold of a product Riemannian manifold has a Riemannian almost-product structure, and investigate properties of integral manifold of distributions of Riemannian almost-product structure, i.e., pseudo-umbilical submanifold and curvature-invariant submanifold.
