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Abstract  

We study non-anti-invariant slant submanifolds of generalized S-space-forms with two structure vector felds in order to know if they inherit the ambient structure. In this context, we focus on totally geodesic, totally umbilical, totally ƒ-geodesic and totally ƒ-umbilical non-anti-invariant slant submanifolds and obtain some obstructions. Moreover, we present some new interesting examples of generalized S-space-forms.

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Abstract  

The distance d G(u, v) between two vertices u and v in a connected graph G is the length of the shortest uv-path in G. A uv-path of length d G(u, v) is called a uv-geodesic. A set X is convex in G if vertices from all ab-geodesics belong to X for any two vertices a, bX. The convex domination number γcon(G) of a graph G equals the minimum cardinality of a convex dominating set. In the paper, Nordhaus-Gaddum-type results for the convex domination number are studied.

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In the present paper parallel submanifolds and focal points of a given submanifold with flat normal bundle are discussed provided that the ambient space has constant sectional curvature. We present shape operators of parallel submanifolds with respect to arbitrary normal vectors. Furthermore, we prove that the focal points of a submanifold with flat normal bundle form totally geodesic hypersurfaces in the normal submanifolds.

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We prove that a diffeomorphism of a manifold with an Ehresmann connection is an automorphism of the Ehresmann connection, if and only if, it is a totally geodesic map (i.e., sends the geodesies, considered as parametrized curves, to geodesies) and preserves the strong torsion of the Ehresmann connection. This result generalizes and to some extent strengthens the classical theorem on the automorphisms of a D-manifold (manifold with covariant derivative).

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In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained.

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Summary  

We introduce a class of submanifolds, namely, Generalized Cauchy--Riemann (GCR) lightlike submanifolds of indefinite Kaehler manifolds. We show that this new class is an umbrella of invariant (complex), screen real [8] and CR lightlike [6] submanifolds. We study the existence (or non-existence) of this new class in an indefinite space form. Then, we prove characterization theorems on the existence of totally umbilical, irrotational screen real, complex and CR minimal lightlike submanifolds. We also give one example each of a non totally geodesic proper minimal GCR and CR lightlike submanifolds.

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While the cadastral and topographic maps tie to the classical reference systems and frames, there will be need to know the relation between the classical and GPS-based networks in a particular country. In this study we discuss the scale factor and azimuth discrepancies between the Hungarian first order triangulation and the national GPS network emphasising their practical significance.The comparison of traditional and GPS derived slope and geodesic distances as well as the comparison of the different azimuths make possible the estimation of the scale and orientation differences of the two systems without the knowledge of height and geoid information which may contain additional errors, too.The estimated −4.34 mm/km mean value reflects the significant scale difference, which is similar to the values derived in neighbour countries. The −2.51 arcsec mean azimuth difference reflects the orientation of the two system.

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Abstract  

Pseudoconnections (or quasi connections) were defined as a generalization of linear connections by Y.-C. Wong in [14], and were developed mainly by Italian and Rumanian mathematicians. The purpose of this paper is to study some properties of a special type of pseudoconnections: the so-called associated pseudoconnections oginirating from linear connections in a very simple manner. In 1 we give a necessary and sufficient condition for a pseudoconnection to be associated, the in 2 we study the geodesics of an associated pseudoconnection. This notion has an immediate application in Finsler geometry, this is the theme of 3. Some questions connecting the curvature of associated pseudoconnections were studied by the author in [7].

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. 1972 π-geodesics and lines of shadow colloquium Math. 26 139 – 146 . [4] Pamfilos , P. 1978

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1991 Morse, M. , A fundamental class of geodesics on any closed surface of genus greater than one, Trans. Amer. Math. Soc. , 26 (1924

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