  We give geometric explanations and proofs of various mirror symmetry
conjectures for $T^{n}$-invariant Calabi-Yau manifolds when instanton
corrections are absent. This uses fiberwise Fourier transformation together
with base Legendre transformation.
  We discuss mirror transformations of
  (i) moduli spaces of complex structures and complexified symplectic
structures, $H^{p,q}$'s, Yukawa couplings;
  (ii) sl(2)xsl(2)-actions;
  (iii) holomorphic and symplectic automorphisms and
  (iv) A- and B-connections, supersymmetric A- and B-cycles, correlation
functions.
  We also study (ii) for $T^{n}$-invariant hyperkahler manifolds.
