David N. Pham

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math.DG2025

On the non-existence of left-invariant hypercomplex structures on $S U (2)^{4 n}$

David N. Pham

Using elementary algebraic arguments, it is shown that $S U (2)^{m} := S U (2) \times \dots \times S U (2)$ ( $m$ times) admits no left-invariant hypercomplex structures for all $m \geq 1$ . T…

math.DG2024

A family of left-invariant SKT metrics on the exceptional Lie group $G_{2}$

David N. Pham

For a complex manifold $(M, J)$ , an SKT (or pluriclosed) metric is a $J$ -Hermitian metric $g$ whose fundamental form $I ¨ := g (J \cdot, \cdot)$ satisfies the condition $\partial\overline…

math.DG2024

Samelson complex structures for the tangent Lie group

David N. Pham

It is shown that for any compact Lie group $G$ (odd or even dimensional), the tangent bundle $T G$ admits a left-invariant integrable almost complex structure, where the Lie group s…

On the non-existence of left-invariant hypercomplex structures on SU(2)4n

A family of left-invariant SKT metrics on the exceptional Lie group G2​

Samelson complex structures for the tangent Lie group

On the non-existence of left-invariant hypercomplex structures on $S U (2)^{4 n}$

A family of left-invariant SKT metrics on the exceptional Lie group $G_{2}$