Accurate trajectory-harps for Kähler magnetic fields. (English) Zbl 1405.53057

Adachi, Toshiaki

J. Math. Soc. Japan 70, No. 4, 1337-1346 (2018).

Summary: In preceding papers we gave estimates on string-lengths, string-cosines and zenith angles of trajectory-harps under the condition that sectional curvatures of the underlying manifold are bounded from above. In this paper we study the cases that equalities hold in these estimates. Refining the previous proofs we give conditions that trajectory-harps are congruent to trajectory-harps on a complex space form.

MSC:

53C22	Geodesics in global differential geometry
53B35	Local differential geometry of Hermitian and Kählerian structures

Keywords:

Kähler magnetic fields; trajectory-harps; string-lengths; string-cosines; zenith angles; tuning-lengths

References:

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