  We show that the quadratic short time behaviour of transition probability is
a natural consequence of the inner product of the Hilbert space of the quantum
system. We prove that Schr\"odinger time evolution between two successive
measurements is not a necessary but only a sufficient condition for predicting
quantum Zeno effect. We provide a relation between the survival probability and
the underlying geometric structure such as the Fubini-Study metric defined on
the projective Hilbert space of the quantum system. This predicts the quantum
Zeno effect even for systems described by non-linear and non-unitary evolution
equations, within the collapse mechanism of the wavefunction during measurement
process. Two examples are studied, one is non-linear Schr\"odinger equation and
other is Gisin's equation and it is shown that one can observe quantum Zeno
effect for systems described by these equations.
