A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form
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A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form. / Lubbe, Felix.
I: Results in Mathematics, Bind 74, Nr. 1, 3, 01.03.2019.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form
AU - Lubbe, Felix
PY - 2019/3/1
Y1 - 2019/3/1
N2 - We consider minimal maps f: M→ N between Riemannian manifolds (M, g M) and (N, g N) , where M is compact and where the sectional curvatures satisfy sec N≤ σ≤ sec M for some σ> 0. Under certain assumptions on the differential of the map and the second fundamental form of the graph Γ(f) of f, we show that f is either the constant map or a totally geodesic isometric immersion.
AB - We consider minimal maps f: M→ N between Riemannian manifolds (M, g M) and (N, g N) , where M is compact and where the sectional curvatures satisfy sec N≤ σ≤ sec M for some σ> 0. Under certain assumptions on the differential of the map and the second fundamental form of the graph Γ(f) of f, we show that f is either the constant map or a totally geodesic isometric immersion.
KW - Bernstein theorem
KW - higher codimension
KW - Minimal maps
UR - http://www.scopus.com/inward/record.url?scp=85056778208&partnerID=8YFLogxK
U2 - 10.1007/s00025-018-0923-5
DO - 10.1007/s00025-018-0923-5
M3 - Journal article
AN - SCOPUS:85056778208
VL - 74
JO - Results in Mathematics
JF - Results in Mathematics
SN - 1422-6383
IS - 1
M1 - 3
ER -
ID: 233725547