| Keywords and phrases: orthogonal almost complex structure, compact Riemann surface with negative constant curvature, round sphere
How to cite this article: Jaeman Kim, Notes on orthogonal almost complex structures on the Riemannian products, JP Journal of Geometry and Topology 31(1) (2025), 19-26. https://doi.org/10.17654/0972415X25003
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References:
[1]A. L. Besse, Einstein Manifolds, Springer, Berlin, 1987.
[2]A. Blanchard, Recherche de structures analytiques complexes sur certaines variétés, C. R. Acad. Sci. Paris 236 (1953), 657-659.
[3]A. Borel and J. P. Serre, Groupes de Lie et puissances reduites de Steenrod, Amer. J. Math. 75 (1953), 409-448.
[4]E. Calabi, Construction and properties of some 6-dimensional almost complex manifold, Trans. Amer. Math. Soc. 87 (1958), 407-438.
[5]P. Chakraborty and A. S. Thakur, Nonexistence of almost complex structures on the product Topology Appl. 199 (2016), 102-110.
[6]J. H. Choi, I. W. Kang, B. H. Kim and Y. Shin, Fibred Riemannian space with almost complex structures, J. Korean. Math. Soc. 46(1) (2009), 171-185.
[7]B. Datta and S. Subramanian, Nonexistence of almost complex structures on products of even-dimensional spheres, Topology Appl. 36(1) (1990), 39-42.
[8]Y. Euh and K. Sekigawa, Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres, J. Korean Math. Soc. 50 (2013), 231-240.
[9]B. Ferlengez, G. Granja and A. Milivojevic, On the topology of the space of almost complex structures on the six sphere, New York J. Math. 27 (2021), 1258-1273.
[10]A. C. Ferreira, Nonexistence of orthogonal complex structures on the round 6-sphere, Differential Geom. Appl. 57 (2018), 87-93.
[11]S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Wiley, Vol. 1, 2, 2009.
[12]C. Lebrun, Orthogonal complex structures on Proc. Amer. Math. Soc. 101 (1987), 136-138.
[13]Z. Tang and W. Yan, Orthogonal almost complex structure and its Nijenhuis tensor, Bull. London Math. Soc. 57 (2025), 1512-1523.
[14]J. A. Wolf, Space of Constant Curvature, AMS Chelsea Publishing, Providence, RI, 2011. |
