GRADIENT VECTOR FIELDS WHICH CHARACTERIZE WARPED PRODUCTS

GRADIENT VECTOR FIELDS WHICH CHARACTERIZE WARPED PRODUCTS

We find what condition on gradient vector fields characterizes warped products, Riemannian products and round spheres. To do this we apply the theory of Jacobi equations without conjugate points to the differential maps of the local one-parameter groups generated by gradient vector fields.

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Veröffentlicht in:Mathematica scandinavica 2001-01, Vol.88 (2), p.182-192
Hauptverfasser: INNAMI, NOBUHIRO, KIM, BYUNG HAK
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Curves
Differential equations
Hypersurfaces
Mathematical constants
Mathematical functions
Mathematics
Matrices
Riemann manifold
Vector fields
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Beschreibung
Zusammenfassung:We find what condition on gradient vector fields characterizes warped products, Riemannian products and round spheres. To do this we apply the theory of Jacobi equations without conjugate points to the differential maps of the local one-parameter groups generated by gradient vector fields.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-14322