Geometric linearization of ordinary differential equations.

Qadir, Asghar

Displaying similar documents to “Geometric linearization of ordinary differential equations.”

Geodesic equations on diffeomorphism groups.

Vizman, Cornelia (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Ermakov's superintegrable toy and nonlocal symmetries.

Leach, P.G.L., Karasu, A., Nucci, M.C., Andriopoulos, K. (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Characterizations of complex space forms by means of geodesic spheres and tubes

J. Gillard (1996)

Colloquium Mathematicae

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We prove that a connected complex space form ( $M^{n}$ ,g,J) with n ≥ 4 can be characterized by the Ricci-semi-symmetry condition ${\tilde{R}}_{X Y} \cdot \tilde{ϱ} = 0$ and by the semi-parallel condition ${\tilde{R}}_{X Y} \cdot σ = 0$ , considering special choices of tangent vectors $X, Y$ to small geodesic spheres or geodesic tubes (that is, tubes about geodesics), where $\tilde{R}$ , $\tilde{ϱ}$ and $σ$ denote the Riemann curvature tensor, the corresponding Ricci tensor of type (0,2) and the second fundamental form of the spheres or tubes and where ${\tilde{R}}_{X Y}$ acts as a derivation.

Nonlocal symmetries and generation of solutions for partial differential equations.

Tychynin, Valentyn, Petrova, Olga, Tertyshnyk, Olesya (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Geodesic reduction via frame bundle geometry.

Bhand, Ajit (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Applications of symmetry methods to the theory of plasma physics.

Cicogna, Giampaolo, Ceccherini, Francesco, Pegoraro, Francesco (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Second-order approximate symmetries of the geodesic equations for the Reissner-Nordström metric and re-scaling of energy of a test particle.

Hussain, Ibrar, Mahomed, Fazal M., Qadir, Asghar (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On the set of homogeneous geodesics of a left-invariant metric.

Szenthe, János (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Free fall motion in an invariant field of forces: the 2D-case.

Pripoae, Cristina-Liliana, Pripoae, Gabriel-Teodor (2009)

Balkan Journal of Geometry and its Applications (BJGA)

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A geometric space without conjugate points.

Bucataru, Ioan, Dahl, Matias F. (2010)

Balkan Journal of Geometry and its Applications (BJGA)

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Symmetric space Cartan connections and gravity in three and four dimensions.

Wise, Derek K. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Lorentzian geometry in the large

John Beem (1997)

Banach Center Publications

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Lorentzian geometry in the large has certain similarities and certain fundamental differences from Riemannian geometry in the large. The Morse index theory for timelike geodesics is quite similar to the corresponding theory for Riemannian manifolds. However, results on completeness for Lorentzian manifolds are quite different from the corresponding results for positive definite manifolds. A generalization of global hyperbolicity known as pseudoconvexity is described. It has important...