Integral curvatures, oscillation and rotation of spatial curves around affine subspaces

Journal of Dynamical and Control Systems

Volumn 2, Issue 2, 1996, Pages 157-191

  Novikov, D ^a   Yakovenko, S ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Frenet curvatures; Geometric probability; Oscillation

Indexed keywords

COMPUTATIONAL GEOMETRY; ESTIMATION; INTEGRAL EQUATIONS; LINEAR ALGEBRA; PROBABILITY;

AFFINE SUBSPACES; EUCLIDEAN SPACE; FRENET CURVATURES; GAUSSIAN CURVATURE; GENERALIZED INFLECTION POINTS; GEODESIC SUBSPACES; INTEGRAL CURVATURES; PROJECTIVE HYPERPLANE; RIEMANNIAN METRIC; SPATIAL CURVES;

CONTROL THEORY;

EID: 0030121206     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02259525     Document Type: Article

References (12)

1. J. Milnor, On total curvature of closed space curves. Math. Scand. 1 (1953), 289-296.
2. D. Alexeevskii, A. Vinogradov, and V. Lychagin, Basic ideas and concepts of differential geometry. Encyclopedia Math. Sci., Geometry-I, Vol. 28, R. V. Gamkrelidze, ed., Springer-Verlag, Berlin, 1991.
3. A. Edelman and E. Kostlan, How many zeros of a random polynomial are real? Bull. Am. Math. Soc. 32 (1994), No. 1, 1-37.
4. I. Fáry, Sur la courbure totale d'une courbe gauche faisant un nœud. Bull. Soc. Math. France 77 (1951), 44-54.
5. W. Fenchel, Über Krümmung und Windung geschlossener Raumkurven. Math. Ann. 101 (1929), 238-252.
6. n and C. J. Dynam. Control Syst. 2 (1996), No. 1, 103-123.
7. D. Novikov and S. Yakovenko, Simple exponential estimate for the number of real zeros of complete Abelian integrals. Ann. Inst. Fourier, Grenoble (1995) (to appear).
8. G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation. Trans. Am. Math. Soc. 24 (1922), 312-324.
9. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. Vol. 2, Sect. 5 (3rd edition), Springer-Verlag, Berlin e.a., 1964.
10. L. Santaló, Integral geometry and geometric probability. Encyclopedia Math. Appl. Vol. 1, Addison-Wesley, Reading, 1976.
11. B. Shapiro, Spaces of linear differential equations and flag manifolds. Math. USSR Izv. 36 (1990), 183-198.
12. M. Shapiro, Topology of the space of nondegenerate closed curves. Math. USSR Izv. 57 (1993), 106-126.