On the structure of geodesic orbit Riemannian spaces

Feb 21, 2017 - geodesics or geodesic orbit manifold (shortly, GO-manifold) if any ... Lie group G admits a Riemannian metric g such that (M,g) is a GO...

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Jul 4, 2012 - as well as on a related class of Riemannian homogeneous spaces having an additional ... homogeneous space G/H with a normal metric ds2.

Apr 6, 2017 - above terms) a well-known criteria of GO-spaces, see other details and useful facts in [25]. Lemma 1 ([20]). A homogeneous Riemannian space ...

Mar 2, 2018 - viated G.O. manifold, if every geodesic is an orbit of a one-parameter group of isometries. .... (2) [Cm(h),m] ⊂ m and Cm(h) is a subalgebra of g.

Oct 24, 2008 - Ы=1/2. The image of the Segré embedding CP1 × CP1 → CP3 (see for exam- ple Ref. 17, p. 55f.) is a 2-dimensional complex quadric in CP3 ; such a quadric is isometric to G+. 2 (IR4). Thereby we see that G+. 2 (IR4) is iso- metric to

Jul 9, 2011 - rise to 2nd-order equations and 1st-order equations (for the even resp. odd coordinates). This explains, at least on an intuitive level, why there might be no geodesic flow ...... 4 The exponential map of a Riemannian superman- ifold. I

Apr 26, 2016 - 2School of Mathematical Sciences and LPMC, Nankai University. Tianjin 300071 ... velopment Fund for Universities and Colleges in Tianjin (no. 20141005), and Doctor fund of Tianjin Normal. University (no. 52XB1305). †S. Deng is the co

Nov 19, 2015 - of “deep learning” and in particular, convolutional neural network (CNN) techniques [17, 27], allowing to ... Learning methods have only recently started penetrating into the 3D shape analysis community in ..... the cotangent formu

Sep 14, 2011 - Riemannian metrics on infinite dimensional manifolds was first noticed on shape space Imm(S1, R2)/ Diff(S1) for the L2-metric in [7, 3.10].

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Aug 30, 2010 - chain complex, the Morse–Witten complex, constructed out of the critical ...... geodesics, hence the natural (actually compulsory) option is ...... A. Bruckner, Differentiation of real functions, 2nd ed, CRM Monograph Series 5,.

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May 17, 2014 - I am grateful to Roman Karasev who provided some references and encouraged me to write down this note, and to Luis. Montejano for information about recent development in the area. 2. Proof of the theorem. Fix n ≥ 1 and denote by ∆

Apr 28, 2011 - geodesics or geodesic orbit manifold (shortly, GO-manifold) if any geodesic γ of M ... L. Vanhecke classified all GO-spaces of dimension ≤ 6.


Jul 2, 2018 - (A,B)∈Cdist(A, sC δg−α(A, B)) ⩾ δg, for all (A, B) ∈ C. Proof. For all (A, B) ∈ C with dist(A, B) < δg, denote by γA,B the minimal unit speed.

Aug 18, 2010 - signature (k, k + m). The symmetry group of frame-rotations in this case is. SO(k, k + m). We will utilise the decomposition where any element, G, can be written G ... act on the pair of null-vectors, while the null-rotations will in g

Feb 20, 2010 - The action is free, discrete and preserves the metric and the quadratic integral ...... xpy(fax + fby + 2fxa + fyb) + pyp2 x(fbx + fcy + fxb + 2fyc) + p3.

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Jan 23, 2014 - Let M be a complete Riemannian manifold. For a point p ∈ M, let TpM be the tangent space at p and expp : TpM → M be the exponential map.

point (we will call such a situation analytic integrability). The regularity of dynamics in the case of ... closed smooth manifolds admit Riemannian metrics with integrable geodesic flows? In other words, we want to ... sphere are equators (i.e., sec

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