Honam Mathematical Journal (호남수학학술지)

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A NOTE ON LOCAL CALIBRATIONS OF ALMOST COMPLEX STRUCTURES

  • Kim, Hyeseon (Department of Mathematics Education, Wonkwang University)
  • Received : 2022.07.18
  • Accepted : 2022.08.07
  • Published : 2022.09.01
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Abstract

In this paper, we study the obstruction on the jets of an almost complex structure J to the existence of a symplectic form ω such that J is compatible with ω. We describe some almost complex structures on ℝ4 and on ℝ6, respectively, that cannot be calibrated by any symplectic forms. In particular, these examples pertain to the model almost complex structure on ℝ4 in [3], and the simple model structure on ℝ6 in [7].

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Acknowledgement

The author thanks to the anonymous referees for their helpful comments.

References

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