The Vamana Avatar of Vishnu ,comparatively speaking,is less dicussed about and the temples for Vamana and Vishnu revealing himself as Trivikrama are limited.
Vamana’s famius temple from where He took His step to measure the world given to Him by Mahabali is in Kerala and there is a Temple for Trivikrama ,when Vishnu measured the world is in Kanchipuram,Tamil Nadu.
The incident narrated about Vamana Avatar is this.
King Mahabali ,Grandson of Prahlada and son of Virochana was found harassing the Dhanavas and Lord Vishnu took the Avatar as Vamana,Dwarf to discipline him.
Mahabali,because of his pious nature and the boons he had received,was difficult to vanquish by any done by warfare.
So,when Mahabali performed a Yagnya,Lord Vishnu,in the form of a Dwarf,Vamana took part in the Yagnya.
It is mandatory to gift Brahmins,the Realized ones,at the end of the Yagnya.
When Vamana,the Dwarf,asked for Three Feet of Land measured by his feet,Mahabali gave him the gift despite the warning by his Guru Sukracharya.
Vamana,it is interpreted,measured the Earth with his first step,the sky with the second and as there was nothing else was available to measure for the third step,Mahabali offered his head as the third step and Vamana pushed Mahabali to Patala Loka and gran.ted him the boon to visit his people once a year.
This visitation by Mahabali is celebrated as Onam Festival in Kerala every year even today.
Now,Indian texts have three meanings,at least.
One is the word to word textual meaning,
The second the philosophical interpretation and the third,
In this incident word by word interpretation narrates the story and conveys that,however mighty one may be,if he is overwhelmed by power and resorts to unrighteous conduct he will be ruined.
If he has bee pious,Divine Grace shall prevent total ruin.
At the philosophical level,one who is steeped in Ahankaara ,the feeling of ‘I’ and attachments to power and riches would be blessed by Divine Grace to remember his Sattivic Swabhava or nature and realize the Reality.
I am providing the historical interpretation below.
Kerala was a part of Tamil kingdom in Lemuria and Lemurians were referred to as the Southerners,Dravida and were reported to be in Patala,down the earth.
The territories we call as south east Asia Australia were in the south.
One must remember that the landmass of the earth was different then.
Lemuria and MU territories encompassed these areas.
Ramayana and Sumerian texts state that Lemurians lived there.
Shiva,who predates Sanatana Dharma was in the south.
Shiva’s trishul marks are found as Nazca lines in Peru.
The Incas,Mayas were the descendants of the Tamils.
You may read more articles on these subjects by following the related articles in the link provided above.
Indra and Virochana( father of Bali) are found in Bali.
Moving to Patala Loka by Bali means that Bali moved further south or down to the areas we now know as SouthEast Asia,Asia-Pacific.
The Tolltechs,Incas,Mayas have a close link with Tamils/Keralites.
Spanish has affinity to Tamil.
‘Prahlada’s son was Virochana and his son was Bali (Mahabali).
When Bali was performing Yagna under supervision of his guru Sukracharya, Vishnu came as Vamana(dwarf or kid) and asked for donation of ‘three pada Bhoomi.’
This is wrongly interpreted as 3 foot land.
Infact it is 3 quarters of Land (pada here is similar to nakshatra pada in vedic astrology, where each nakshatra is divided into 4 padas [quarters]).
At that time, Bali was ruling over Asia, Europe and Africa. So he donated these 3 human inhabitated lands to Vamana and decided to leave.
Vamana was satisfied with Bali and gave him a boon of becoming next Indra, but until then he has to settle in Patala loka and perform yagnas….
Bali travelled towards east in a ship with his men in same path as described by Sugreeva in Ramayana and settled in South America.
On this path he discovered Sutala (Islands in South East Asia and Australia), Talatala (Antarctica) and Patala (South America).
His men created settlements even in Mahatala (North America)…
People residing in these places were known as ‘Talatalak’. This name corrupted to ‘Toltec’.
Toltecs still exist in Mexico of South America. Maya (founder of Mayan Calendar) was an engineer, who built three cities for Bali.
Maya built 3 cities for his king Bali and thus Bali was called as ‘tribhuvanak‘ (lord of 3 cities). This word later got corrupted to Tiahuanaco in Mexico.
The Nazca Lines in USA are supposed to be air plane landing markings made by Bali.
Patala was later inhabitated by people called as ‘Sarpa’, who went there on behest of Waman to keep
watch on Bali’s activities. Total seven colonies were new, therefore they were called as ‘Navatala’. Nava means new and Tala means colony. This word ‘Navatala’, in a corrupt form as ‘Nahuatl’, still exists in the South America. People residing in Mexico and around are known as ‘Nava’ and their language is called as ‘Nahuatl’.
Reference and citation.