ON THE NUMBER OF CONNECTED COMPONENTS IN THE SPACE OF CLOSED NONDEGENERATE CURVES ON S n

@article{Shapiro1991ONTN,
  title={ON THE NUMBER OF CONNECTED COMPONENTS IN THE SPACE OF CLOSED NONDEGENERATE CURVES ON S n},
  author={B. Shapiro and M. Shapiro},
  journal={Bulletin of the American Mathematical Society},
  year={1991},
  volume={25},
  pages={75-79}
}
The main definition. A parametrized curve γ : I → R is called nondegenerate if for any t ∈ I the vectors γ′(t), . . . , γ(t) are linearly independent. Analogously γ : I → S is called nondegenerate if for any t ∈ I the covariant derivatives γ′(t), . . . , γ(t) span the tangent hyperplane to S at the point γ(t) ( compare with the notion of n-freedom in [G]). Fixing an orientation in R or S we call a nondegenerate curve γ right-oriented if the orientations of γ′, . . . , γ coincide with the given… Expand

References

SHOWING 1-10 OF 14 REFERENCES
Partial Differential Relations
Ovsienko, Symplectic leaves of Gelfand-Dikii’s brackets and homotopical classes of nondegenerate curves, Funct
  • Analiz i ego Priloz
  • 1990
Symplectic leaves of Gelfand-Dikii's brackets and homotopical classes of nondegenerate curves, Funct. Analiz i ego Priloz
  • Symplectic leaves of Gelfand-Dikii's brackets and homotopical classes of nondegenerate curves, Funct. Analiz i ego Priloz
  • 1990
Hamenstadt, Zur Theorie von Carno-Caratheodory Metriken und ihren Anwendungen
  • Bonner Math. Schr
  • 1987
Zur Theorie von Carno-Caratheodory Metriken und ihren Anwedungen
  • Bonner Math. Schr
  • 1987
Zur Theorie von Carno-Caratheodory Metriken und ihren Anwendungen
  • Bonner Math. Schr
  • 1987
...
1
2
...