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We investigate doubled (generalized) complex structures in $2D$-dimensionalBorn geometries where T-duality symmetry is manifestly realized. We show thatK\"{a}hler, hyperk\"{a}hler, bi-hermitian and bi-hypercomplex structures ofspacetime are implemented in Born geometries as doubled structures. We findthat the Born structures and the generalized K\"{a}hler (hyperk\"{a}hler)structures appear as subalgebras of bi-quaternions and split-tetra-quaternions.We find parts of these structures are classified by Clifford algebras. We thenstudy the T-duality nature of the worldsheet instantons in Born sigma models.We show that the instantons in K\"{a}hler geometries are related to those inbi-hermitian geometries in a non-trivial way.

Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models