Found 73 Documents (Results 1–73)
Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(\operatorname{SU}(1,1)\times \mathbb{R}\) and \(\operatorname{SO}_0(2,1)\times \mathbb{R}\) with three-dimensional generating distributions. (English. Russian original) Zbl 07825247
Sib. Math. J. 65, No. 2, 295-315 (2024); translation from Sib. Mat. Zh. 65, No. 2, 295-317 (2024).
A Grassmann manifold handbook: basic geometry and computational aspects. (English) Zbl 1532.53001
Adv. Comput. Math. 50, No. 1, Paper No. 6, 51 p. (2024); correction ibid. 50, No. 2, Paper No. 20, 2 p. (2024).
The conjugate locus in convex 3-manifolds. (English) Zbl 07731292
Reviewer: Georges Habib (Fanar)
Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups \(SU(2)\times{ \mathbb{R} }\) and \(SO(3)\times{ \mathbb{R} }\) with three-dimensional generating distributions. (English. Russian original) Zbl 1517.53037
Sib. Math. J. 64, No. 3, 575-592 (2023); translation from Sib. Mat. Zh. 64, No. 3, 521-539 (2023).
Reviewer: Andreas Arvanitoyeorgos (Pátra)
The structure of the conjugate locus of a general point on ellipsoids and certain Liouville manifolds. (English) Zbl 1492.53054
Reviewer: Emanuel-Ciprian Cismaş (Timişoara)
Short geodesics losing optimality in contact sub-Riemannian manifolds and stability of the 5-dimensional caustic. (English) Zbl 1423.53034
Reviewer: Peibiao Zhao (Nanjing)
Generic singularities of the 3D-contact sub-Riemannian conjugate locus. (Singularités génériques du lieu conjugé en géométrie sous-riemannienne dans le cas 3D-contact.) (English. Abridged French version) Zbl 1485.53037
Reviewer: Mihail Banaru (Smolensk)
The conjugate locus on convex surfaces. (English) Zbl 1419.53005
Reviewer: Benjamin McKay (Cork)
Blaschke Finsler manifolds and actions of projective Randers changes on cut loci. (English) Zbl 1416.53070
Reviewer: V. K. Chaubey (Gorakhpur)
Bishop and Laplacian comparison theorems on Sasakian manifolds. (English) Zbl 1407.53046
Reviewer: Neda Bokan (Beograd)
Central conjugate locus of 2-step nilpotent Lie groups. (English) Zbl 1412.53063
Reviewer: Adriana Nicolae (Cluj-Napoca)
Sub-Riemannian distance on the Lie group \(\operatorname {SO}_0(2,1)\). (English. Russian original) Zbl 1375.53043
St. Petersbg. Math. J. 28, No. 4, 477-489 (2017); translation from Algebra Anal. 28, No. 4, 62-79 (2016).
Reviewer: Hubert Gollek (Berlin)
Locally isometric coverings of the Lie group \(\mathrm{SO}_0(2,1)\) with special sub-Riemannian metric. (English. Russian original) Zbl 1365.53037
Sb. Math. 207, No. 9, 1215-1235 (2016); translation from Mat. Sb. 207, No. 9, 35-56 (2016).
Reviewer: Hubert Gollek (Berlin)
Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\). (English. Russian original) Zbl 1347.53028
Sib. Math. J. 57, No. 3, 411-424 (2016); translation from Sib. Mat. Zh. 57, No. 3, 527-542 (2016).
(Locally) shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SO}_0(2,1)\). (English. Russian original) Zbl 1335.53038
St. Petersbg. Math. J. 27, No. 1, 1-14 (2016); translation from Algebra Anal. 27, No. 1, 3-22 (2015).
Reviewer: V. V. Gorbatsevich (Moskva)
Metrics with equatorial singularities on the sphere. (English) Zbl 1305.53040
Reviewer: Constantin Călin (Iaşi)
Riemannian metrics on 2D-manifolds related to the Euler-Poinsot rigid body motion. (English) Zbl 1293.49040
Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric. (English) Zbl 1261.58009
Reviewer: Vladimir Balan (Bucureşti)
Cut loci and conjugate loci on Liouville surfaces. (English) Zbl 1231.53035
Reviewer: Zdeněk Dušek (Olomouc)
Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry. (English) Zbl 1201.35087
Rigidity for closed manifolds with positive curvature. (English) Zbl 1178.53033
Reviewer: Zdeněk Dušek (Olomouc)
MSC:
53C20
Conjugate and cut loci of a two-sphere of revolution with application to optimal control. (English) Zbl 1184.53036
Reviewer: Gábor Tóth (Camden)
Global decomposition of vector field on Riemannian manifolds along natural coordinates. (English) Zbl 1168.53315
Maxwell strata and caustics. (English) Zbl 1143.58017
Brasselet, Jean-Paul (ed.) et al., Singularities in geometry and topology. Proceedings of the Trieste singularity summer school and workshop, ICTP, Trieste, Italy, August 15–September 3, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-022-3/hbk). 787-824 (2007).
Reviewer: Richárd Rimányi (Chapel Hill)
Jacobi’s last geometric statement extends to a wider class of Liouville surfaces. (English) Zbl 1124.53015
Reviewer: George F. Nassopoulos (Athens)
The cut loci and the conjugate loci on ellipsoids. (English) Zbl 1076.53042
Reviewer: Udo Hertrich-Jeromin (Bath)
The time-like cut locus and conjugate points in Lorentz 2-step nilpotent Lie groups. (English) Zbl 1074.53055
Reviewer: Rainer Schimming (Greifswald)
MSC:
53C50
On the last geometric statement of Jacobi. (English) Zbl 1073.53007
Reviewer: Wolfgang Kühnel (Stuttgart)
Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function. (English) Zbl 1042.53045
Geometry of manifolds. Reprint of the 1964 original. (English) Zbl 0984.53001
Providence, RI: AMS Chelsea Publishing. xii, 273 p. (2001).
Reviewer: A.Akutowicz (Berlin)
On the Dido problem and plane isoperimetric problems. (English) Zbl 0977.53068
Reviewer: S.Gomis (Murcia)
Sub-Riemannian geometry: the Martinet case. (English) Zbl 0967.53020
Jurdjevic, V. (ed.) et al., Geometric control and non-holonomic mechanics. Proceedings of a conference, Mexico City, Mexico, June 19-21, 1996. Providence, RI: American Mathematical Society. CMS Conf. Proc. 25, 79-100 (1998).
MSC:
53C17
Two affine structures imposed in the polynomials with degree four. (English) Zbl 0909.30003
Reviewer: J.Matkowski (Bielsko-Biała)
Coherent states and geometry. (English) Zbl 0958.32016
Reviewer: Vasile Brînzănescu (Bucureşti)
On the geometry of complex Grassmann manifold, its noncompact dual and coherent states. (English) Zbl 0947.53021
Sub-Riemannian sphere in Martinet flat case. (English) Zbl 0902.53033
Reviewer: C.Udrişte (Bucureşti)
The nonspacelike cut locus revisited. (English) Zbl 0897.53036
Reviewer: D.E.Allison (Greeley)
Closed geodesic arcs in Aleksandrov spaces. (English) Zbl 0889.53027
Stoka, Marius I. (ed.), Second international conference in stochastic geometry, convex bodies and empirical measures, Agrigento, Italy, September 9–14, 1996. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 50, 425-430 (1997).
Reviewer: C.-L.Bejan (Iaşi)
The cut locus of an ellipsoid. (English) Zbl 0888.52008
Reviewer: H.Martini (Chemnitz)
MSC:
52A40
Some consequences of the nature of the distance function on the cut locus in a Riemannian manifold. (English) Zbl 0892.53021
Reviewer: D.Barden (Cambridge)
Conjugate points and closed geodesic arcs on convex surfaces. (English) Zbl 0866.53050
Reviewer: C.-L.Bejan (Iaşi)
Criteria for multiple imaging in Lorentzian manifolds. (English) Zbl 0852.53048
Reviewer: M.Kriele (Berlin)
The cut locus and conjugate points of geodesics in Lorentz and Riemannian spaces. (Russian. English summary) Zbl 0866.53051
Reviewer: W.Waliszewski (Łódź)
MSC:
53C50
General conjugate loci are not closed. (English) Zbl 0811.53043
Greene, Robert (ed.) et al., Differential geometry. Part 3: Riemannian geometry. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 3, 465-478 (1993).
Reviewer: W.Ballmann (Bonn)
MSC:
53C22
On stability of a certain minimal submanifold in \(SU(3)/SO(3)\). (English) Zbl 0799.53072
Reviewer: C.Olmos (Córdoba)
Ray paths and caustics on a slightly oblate ellipsoid. (English) Zbl 0711.53005
Reviewer: H.Guggenheimer
On conjugate and cut loci. (English) Zbl 0683.53043
Global differential geometry, MAA Stud. Math. 27, 140-169 (1989).
Reviewer: Bernd Wegner
Geometric properties of unitary-symmetric Kähler manifolds. (English) Zbl 0671.53047
Reviewer: J.Girbau
Local study of cut loci of closed surfaces without conjugate points. (English) Zbl 0653.53028
Reviewer: Y.Shikata
Cut locus in a Riemannian manifold. (English) Zbl 0607.53029
Reviewer: G.Tsagas
Certain minimal or homologically volume minimizing submanifolds in compact symmetric spaces. (English) Zbl 0581.53044
Reviewer: T.Ochiai
Symmetric cut loci in Riemannian manifolds. (English) Zbl 0563.53037
MSC:
53C22
Some considerations on the cut locus of a Riemannian manifold. (English) Zbl 0544.53036
Geometry of geodesics and related topics, Proc. Symp., Tokyo 1982, Adv. Stud. Pure Math. 3, 29-46 (1984).
Reviewer: P.Walczak
On the structure of space-time caustics. (English) Zbl 0557.53036
Reviewer: H.Seifert
Correction to ”On conjugate loci and cut loci of compact symmetric space. I”. (English) Zbl 0516.53052
MSC:
53C35
Notes on complete noncompact Riemannian manifolds with convex exhaustion functions. (English) Zbl 0488.53030
MSC:
53C20
Conjugate and cut loci and the Cartan-Ambrose-Hicks theorem. (English) Zbl 0451.53028
Indiana Univ. Math. J. (to appear).
MSC:
53C20
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