romance between married women and doctor in an island

hi all,
trying to remember the name of this book, it starts with someone telling her most older memory about a man she met, this men tells her the story of his life and at the end she thinks this men is her father...
The story of the mens life is something like he is a doctor on an island and he meets a married women, he falls in love with her, they decide to run away. The day they run away the husband is found dead. The women asks her lover the doctor to go back to get something in her house and the doctor gets arrested for murder. The women goes away.
Thanks in advance,
Pedro

I found it! The title is:
The Blue Afternoon
and a better description here:
https://en.wikipedia.org/wiki/The_Blue_Afternoon

So glad you found it! Thanks for coming back and letting us know.

Touchstone: The Blue Afternoon