Two theorems on extensions of holomorphic mappings

Griffiths, Phillip

doi:10.1007/bf01418742

Cited by 59 publications

(21 citation statements)

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“…These results are analogous to theorems on extending holomorphic maps into manifolds with holomorphic sectional curvatures < 0 obtained by the author [5] and independently by Griffiths [3]. A similar type of result on meromorphic extension of equidimensional maps has been given by Griffiths [2,Theorem D].…”

supporting

confidence: 74%

Extension of holomorphic maps

Shiffman¹

1976

Bull. Amer. Math. Soc.

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In this note we announce results on extending holomorphic maps into compact complex manifolds that satisfy certain curvature conditions. These results are analogous to theorems on extending holomorphic maps into manifolds with holomorphic sectional curvatures < 0 obtained by the author [5] and independently by Griffiths [3]. A similar type of result on meromorphic extension of equidimensional maps has been given by Griffiths [2, Theorem D].Let E be a hermitian holomorphic vector bundle on a complex manifold M. Let R(v, w, s, t ) denote the curvature tensor for the hermitian connection on E, The analogous result for k -1 is given in [5, Lemma 3] where M is allowed to be complete instead of compact (see also [3] ).

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supporting

confidence: 74%

Extension of holomorphic maps

Shiffman¹

1976

Bull. Amer. Math. Soc.

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“…This lemma is essentially proved by Griffiths [2] when M is a complex manifold having a complete Hermitian metric all of whose holomorphic sectional curvatures are nonpositive.…”

Section: Consider Hyper Spheres B With the Center P And S Whose Boumentioning

confidence: 98%

Mappings into hyperbolic spaces

Kwack¹

1973

Bull. Amer. Math. Soc.

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In this note we state some results on extensions of holomorphic mapings into hyperbolic spaces. A theorem involves extending holomorphic mappings to a domain of holomorphy. An extension problem of holomorphic mappings into a taut complex space was considered by FujimotoAnother result is that the space of all meromorphic mappings from a complex space X into a hyperbolically imbedded space in Y is relatively compact in the space of all meromorphic mappings from X into Y.A relatively compact complex space M is said to be hyperbolically imbedded in a complex space Y if for all sequences {p n } and {q n } in M such that p n -+ peM and g w -> qeM and such (1970). Primary 32A10, 32H20. AMS (MOS) subject classifications

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“…où a ç C* : |a| < 1 X est homogène compacte et la projection canonique p : C 2 \ {0} -> X ne se prolonge pas en 0 (même méromorphiquement) puisque l'adhérence Gp du graphe de p dans C 2 contient {0} x X ; [6]. Démonstration.…”

Section: (^1^2) =(Az^az^)unclassified

Prolongement d'applications holomorphes

Krachni¹

1990

Bul. Soc. Math. France

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Two theorems on extensions of holomorphic mappings

Cited by 59 publications

References 12 publications

Extension of holomorphic maps

Extension of holomorphic maps

Mappings into hyperbolic spaces

Prolongement d'applications holomorphes

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