1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively defined in the Einstein, telepa...

Part 1. Geometry of Curves We assume that we are given a parametric space curve of the form (1) x(u) =   x 1 (u) x 2 (u) x 3 (u)   u 0 ≤ u ≤ u 1 and that the following derivatives exist and are continuous (2) x (u) = dx du x (u) = d 2 x du 2 1. Arc Length The total arc length of the curve from its starting point x(u 0) to some point x(u) on the curve is defined to be (3) s(u) = u u 0 √ x ·x...

The main objective for this thesis is the construction of a tensor bundle on a diffeological space X. Thereby getting access to the exterior bundle of antisymmetric tensors on X, and smooth sections here on i.e. differential forms. We shall list certain requirements that any reasonable tensor bundle on a diffeological space should fulfil. And show that the given construction fulfil these requir...

In less than two pages (pp. 54–55) the Campbell-Baker-Hausdorff formula is taken care of, in a proof containing exactly forty-eight English words: the rest is algebraic manipulation. For some of us, myself included, this is an exposition devoutly-to-be-wished; for the complementary set of readers it’s something a lot less than palatable. So, given that Peter W. Michor’s Topics in Differential G...

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These notes are from a lecture course Di erentialgeometrie und Lie Gruppen which has been held at the University of Vienna during the academic year again in and in WS It is not yet complete and will be enlarged during the year In this lecture course I give complete de nitions of manifolds in the beginning but beside spheres examples are treated extensively only later when the theory is develope...

1 Geometry of Manifolds 3 1.1 Definition of smooth manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Tangent space to a manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Vector fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Smooth functions on manifolds, partitions of unity. . . . . . . . . . . . . . . 22 1.5 Immers...

in this paper, a useful classification of all lie subalgebras of a given lie algebraup to an inner automorphism is presented. this method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. after main results, we have applied this procedure for classifying the lie subalgebras of some examples of lie al...