On holomorphic mappings between almost Hermitian manifolds

Masood, Kirollos

doi:10.1090/proc/15209

On holomorphic mappings between almost Hermitian manifolds
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Proc. Amer. Math. Soc. 149 (2021), 687-699 Request permission

Abstract:

Our goal is to utilize the techniques of Xiaokui Yang, Valentino Tosatti, and Chenjie Yu to establish a Liouville-type result for almost complex manifolds. The transition to the non-integrable setting is delicate, so we devote one section to discussing the key differences, and another to introducing the necessary tools. Afterwards, we present a proof of our main theorem.

References

Werner Ballmann, Lectures on Kähler manifolds, ESI Lectures in Mathematics and Physics, European Mathematical Society (EMS), Zürich, 2006. MR 2243012, DOI 10.4171/025
Andrzej Derdzinski, Kähler geometry from a Riemannian perspective, 2018, URL: https://people.math.osu.edu/derdzinski.1/courses/7721/kg.pdf.
Charles Ehresmann and Paulette Libermann, Sur les structures presque hermitiennes isotropes, C. R. Acad. Sci. Paris 232 (1951), 1281–1283 (French). MR 40790
Daniel Huybrechts, Complex geometry, Universitext, Springer-Verlag, Berlin, 2005. An introduction. MR 2093043
Boris Kruglikov, Dozen definitions of the Nijenhuis tensor, 2018, URL: http://www.math.uit.no/ansatte/boris/Images/1/12DEF-NJ.pdf.
Andrei Moroianu, Lectures on Kähler geometry, London Mathematical Society Student Texts, vol. 69, Cambridge University Press, Cambridge, 2007. MR 2325093, DOI 10.1017/CBO9780511618666
Gang Tian, Canonical metrics in Kähler geometry, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2000. Notes taken by Meike Akveld. MR 1787650, DOI 10.1007/978-3-0348-8389-4
Valentino Tosatti, A general Schwarz lemma for almost-Hermitian manifolds, Comm. Anal. Geom. 15 (2007), no. 5, 1063–1086. MR 2403195
Xiaokui Yang, RC-positivity and the generalized energy density I: Rigidity, arXiv e-prints, Oct 2018. arXiv:1810.03276.
Xu-Qian Fan, Luen-Fai Tam, and Chengjie Yu, Product of almost-Hermitian manifolds, J. Geom. Anal. 24 (2014), no. 3, 1425–1446. MR 3223560, DOI 10.1007/s12220-012-9379-0
ChengJie Yu, Curvature identities on almost Hermitian manifolds and applications, Science China Mathematics, 60(2):285–300, Feb 2017, http://dx.doi.org/10.1007/s11425-016-0022-6
Fangyang Zheng, Complex differential geometry, AMS/IP Studies in Advanced Mathematics, vol. 18, American Mathematical Society, Providence, RI; International Press, Boston, MA, 2000. MR 1777835, DOI 10.1090/amsip/018