What Are The Different Health Fields In Which Eating Tomatoes Is Useful?

Don't know what you mean by 'different fields' but they're definitely very rich in Vitamin C which is good for your bones and teeth. Research has also suggested that women who include tomatoes in their diet, will have a lesser risk of a miscarriage. However, people with kidney problems should stay away from them or have them without the peel since it's believed to aggravate their problems.

Tomatoes are rich in vitamins beta-carotene, vitamin C, vitamin A, vitamin B6,vitamine E.
It's consumption is believed to benefit the heart among other things.
Carotenoid Lycopene, one of nature's most powerful antioxidants,is present in tomatoes is believed to reduce the risk of certain forms of cancer(like prostate, lung, and stomach).
Antioxidants may protect against certain chronic diseases such as cancer,
        coronary heart disease, and cataracts.
Tomatoes are also high in potassium but very low in sodium which means they help combat high blood pressure and fluid retention.Tomato extract branded as Lycomato is now also being promoted for treatment of high blood pressure.
Moreover tomatoes contain dietary fiberand has no cholesterol.