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Let $(X^n, \check{X}^n)$ be a mirror pair of an $n$-dimensional complex torus$X^n$ and its mirror partner $\check{X}^n$. Then, a simple projectively flatbundle $E(L,\mathcal{L})\rightarrow X^n$ is constructed from each affineLagrangian submanifold $L$ in $\check{X}^n$ with a unitary local system$\mathcal{L} \rightarrow L$. In this paper, we first interpret these simpleprojectively flat bundles $E(L,\mathcal{L})$ in the language of factors ofautomorphy. Furthermore, we give a geometric interpretation for exact trianglesconsisting of three simple projectively flat bundles $E(L,\mathcal{L})$ andtheir shifts by focusing on the dimension of intersections of the correspondingaffine Lagrangian submanifolds $L$. Finally, as an application of thisgeometric interpretation, we discuss whether such an exact triangle on $X^n$($n \geq 2$) is obtained as the pullback of an exact triangle on $X^1$ by asuitable holomorphic projection $X^n \rightarrow X^1$.

Geometric interpretation for exact triangles consisting of projectively flat bundles on higher dimensional complex tori