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Oscillation criteria for self-adjoint second-order differential systems and ”Principal sectional curvatures”. (English) Zbl 0443.34029

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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[1] Calabi, E; Hartman, P, On the smoothness of isometries, Duke math. J., 37, 741-750, (1970) · Zbl 0203.54304
[2] Cheeger, J; Ebin, D.G, Comparison theorems in Riemann geometry, (1975), American Elsevier New York · Zbl 0309.53035
[3] Chern, S.S; Kuiper, N.H, Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space, Ann. of math., 56, 422-430, (1952) · Zbl 0049.23402
[4] Gromoll, D; Klingenberg, W; Meyer, W, Riemannsche geometrie im grossen, () · Zbl 0155.30701
[5] Etgen, G.J; Lewis, R.T, Positive functionals and oscillation criteria for differential systems, (), 245-275
[6] Hartman, P, Linear second order systems of ordinary differential equations and geodesic flows, (), 293-316
[7] Hartman, P, On the isometric immersions in Euclidean space of manifolds with nonnegative sectional curvatures, II, Trans. amer. math. soc., 147, 529-540, (1970) · Zbl 0194.22702
[8] Hartman, P, Ordinary differential equations, (1973), S. M. Hartman Baltimore · Zbl 0125.32102
[9] Klingenberg, W, Über riemannsche mannigfaltigkeiten mit positiver krümmung, Comment. math. helv., 35, 47-54, (1961) · Zbl 0133.15005
[10] Klingenberg, W, Über riemannsche mannigfaltigkeiten mit nach oben beschränkter krümmung, Ann. mat. pura appl., 60, 49-60, (1963), (4) · Zbl 0112.13603
[11] Myers, S.B, Riemannian manifolds with positive Mean curvature, Duke math. J., 8, 401-404, (1941) · Zbl 0025.22704
[12] Simons, W, Disconjugacy criteria for systems of self-adjoint differential equations, J. London math. soc., 6, 373-381, (1973), (2) · Zbl 0256.34041
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