A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

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

Harvard

Lubbe, F 2019, 'A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form', Results in Mathematics, bind 74, nr. 1, 3. https://doi.org/10.1007/s00025-018-0923-5

APA

Lubbe, F. (2019). A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form. Results in Mathematics, 74(1), [3]. https://doi.org/10.1007/s00025-018-0923-5

Vancouver

Lubbe F. A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form. Results in Mathematics. 2019 mar. 1;74(1). 3. https://doi.org/10.1007/s00025-018-0923-5

Author

Lubbe, Felix. / A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form. I: Results in Mathematics. 2019 ; Bind 74, Nr. 1.

Bibtex

@article{1eb990ac7d5e4bd5a26e45a17d1d4327,
title = "A Bernstein Theorem for Minimal Maps with Small Second Fundamental Form",
abstract = "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.",
keywords = "Bernstein theorem, higher codimension, Minimal maps",
author = "Felix Lubbe",
year = "2019",
month = mar,
day = "1",
doi = "10.1007/s00025-018-0923-5",
language = "English",
volume = "74",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Birkhauser Verlag Basel",
number = "1",

}

RIS

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