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...

0 downloads 9 Views 280KB Size

Recommend Documents

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 - the complex quadrics (which are symmetric spaces of rank 2) in Ref. 3, and ..... S. Klein, Totally geodesic submanifolds of the complex quadric, ...

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

Feb 20, 2015 - we can characterize sub-Riemannian geodesics as the horizontal lifts of ... also appears as a hypothesis in the second approach to curva-.

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

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

Sep 22, 2017 - In order to formalize these ideas, let us begin with some basic preliminaries. Let (M,g) be a .... So, by the Inverse Function Theorem, expq : U ⊂ TqM → V ⊂ M is a diffeomor- phism between certain ... U ⊂ TqM. So, if we define.

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].

To talk about differential geometry on the quantum space, we should have A extended to the ...... Roughly speaking, θ corresponds to the azimuthal angel on S2.

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,.

Mar 26, 2014 - n ≥ 2, and let f be a function which support does not contain the ... about WF(f) near the conormal bundle N∗γ0 of γ0. ...... [38] M. E. Taylor.

Feb 12, 2016 - The authors would like to thank Marco Radeschi for interesting discussions and useful comments. 2. Preliminaries. 2.1. Orbit spaces and strata.

Sep 23, 2018 - such a way. However, it seems difficult to study metric spaces with unit ball graphs ... net. 3-sun. Figure 3: Obstructions for unit interval graphs.

Nov 19, 2014 - arXiv:1411.5355v1 [math-ph] 19 Nov 2014. The classical ... energy surface H = E can be mapped topologically one-to-one into the unit tangent.

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.


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.

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 ∆

Dec 3, 2008 - Claim: Let X be a proper, geodesic, Ptolemy metric space. Let further ..... If affine functions separate points, then Ao : X → Eo is an isometry.

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.

Jun 28, 2013 - ... Solodovnikov, A.S.: Spaces with common geodesics, Tr. Semin. Vektor. Tenzor. ... [35] Vranceanu, G.: Leçons de geometri différentielle, vol.