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The tangent structure

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  • In the context of Riemannian geometry, the tangent bundle TM of a Riemannian manifold (M, g) was classically equipped with the Sasaki metric gS , which was introduced in 1958 by Sasaki. In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.

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  • Classical differential geometry is the approach to geometry that takes full advantage of the introduction of numerical coordinates into a geometric space. This use of coordinates in geometry was the essential insight of Rene Descartes that allowed the invention of analytic geometry and paved the way for modern differential geometry. The basic object in differential geometry (and differential topology) is the smooth manifold. This is a topological space on which a sufficiently nice family of coordinate systems or "charts" is defined.

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  • In this volume I present some examples of tangents to curves, tangent planes to surfaces, elementary integrals and Extrema, cf. also Calculus 2b, Functions of Several Variables. Since my aim also has been to demonstrate some solution strategy I have as far as possible structured the examples according to the following form A Awareness, i.e. a short description of what is the problem. D Decision, i.e. a reflection over what should be done with the problem. I Implementation, i.e. where all the calculations are made. C Control, i.e. a test of the result....

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  • The purpose of the present paper is to study, using the Tachibana operator, the complete lifts of affinor structures along a pure cross-section of the tensor bundle and to investigate their transfers. The results obtained are to some extent similar to results previously established for tangent (cotangent) bundles.

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  • In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that the 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures.

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  • This paper deals with the relative nullity distributions of lightlike hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field. Theorems on parallel vector fields are obtained. We give characterization theorems for the relative nullity distributions as well as for Einstein, totally contact umbilical and flat lightlike hypersurfaces.

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